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add zine example
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‎site/_quarto.yml‎

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- text: |
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<script data-goatcounter="https://clojurecivitas.goatcounter.com/count" async src="//gc.zgo.at/count.js"></script>
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format-links:
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- html
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- format: typst
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text: "PDF"
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icon: file-pdf
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brand:
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light: brand-light.yml
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dark: brand-dark.yml

‎src/math/stats/quantquestions/what_are_the_odds/cheat_zine.clj‎

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^:kindly/hide-code
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(ns math.stats.quantquestions.what-are-the-odds.cheat-zine
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{:clay {:title "A Survival Themed Probability Cheatsheet Zine"
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;; NOTE: `:static true` tells Clay to export SVGs as images so they can be compiled into the PDF.
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:kindly/options {:static true
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:kinds-that-hide-code #{:kind/var :kind/hiccup}}
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;; NOTE: Typst configuration. Typst is a PDF compiler.
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;; See the {=typst} block at the start of the content,
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;; where the zen-zine plugin is activated.
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:quarto {:format {:typst {:papersize :us-letter
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:fontsize "8pt"}}
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;; NOTE: overriding theme to make more printer friendly
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:theme :flatly
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:brand false
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:number-sections false
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:image "cheat_zine.png"
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:author [:timothypratley]
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:description "A printable PDF of an 8-panel foldable probability zine built with Clay."
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:abstract "This zine sheet folds into 8 small pages. Space is tight, so it focuses on a few core ideas instead of full definitions; counting outcomes, choosing the right denominator, using AND/OR/NOT, and conditional probability. The layout and fold structure are handled by the zen-zine Typst plugin. The zine is for quick learning and quick checks of understanding, such as a short discussion with a nephew or niece."
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:date "2026-06-20"
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:category :stats
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:tags [:stats :probability :zine :print :typst]}}}
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;; NOTE: Plotje output is SVG, which is perfect to use with `:static true` for PDF.
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(:require [scicloj.plotje.api :as pj]))
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;; ```{=typst}
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;; #import "@preview/zen-zine:0.4.0": zine8
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;; #show: zine8
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;; ```
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;; # Will You Survive?
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;; ### Island Survival Guide
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;; You are stranded on an island.
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;; The difference between rescue and disaster lies in the data.
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;; This is your survival guide to probability and statistics.
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;; Learn the patterns, and maybe you will get rescued.
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;; ::: {.content-visible when-format="html"}
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;; ::: {.callout-note}
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;; This page is a companion to a printable foldable zine.
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;; See [the PDF](cheat_zine.pdf) to view the 8-panel print layout.
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;; :::
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;; :::
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;; ![](island.svg)
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;; {{< pagebreak >}}
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;; ## Enumerate and count
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;; $P(E) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$
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;; Check 10 nearby trees.
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;; Count the outcomes you care about, then divide by the number of trees.
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;; Enumeration means listing possible outcomes so you can count them.
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^:kindly/hide-code
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(let [fruiting? #{1 7}
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step 22]
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(into
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^:kind/hiccup
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[:svg {:viewBox "0 0 260 84" :width "100%" :style {:background "#ffffff"}}
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[:text {:x 120 :y 16 :text-anchor "middle" :font-size 14 :font-weight 700 :fill "#111827"}
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"Tree Fruiting Probability"]]
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(concat
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(for [i (range 10)
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:let [x (+ 20 (* i step))
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fruit? (contains? fruiting? i)]]
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[:g
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[:rect {:x x :y 28 :width 16 :height 16 :rx 3
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:fill (if fruit? "#fef3c7" "#e5e7eb")
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:stroke (if fruit? "#d97706" "#9ca3af")}]
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(when fruit?
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[:text {:x (+ x 8) :y 40 :text-anchor "middle" :font-size 8 :fill "#92400e"}
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"F"])])
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[[:text {:x 120 :y 62 :text-anchor "middle" :font-size 9 :fill "#92400e"}
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"Observed fruiting = 2/10"]])))
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;; You sampled 10 trees, but the island has over 100 trees.
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;; So $\frac{2}{10}=0.2$ is a sample-based guess: useful for describing what you observed and predicting future observations.
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;; Statistics use past observations (like 2 of 10 trees) to estimate a probability.
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;; Probability uses that estimate to predict what will happen at the next tree.
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;; Probability rules show how to combine predictions into complex scenarios.
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;; {{< pagebreak >}}
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;; ## The AND Rule
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;; $P(A \text{ and } B) = P(A) \times P(B)$
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;; You make two foraging stops before dark; how much fruit should you expect?
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;; Linked events shrink your chances; multiply the probabilities along the branches. Each requirement filters out more possibilities, so you need both to happen.
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^:kindly/hide-code
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(let [cell 12
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pad 34
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cols 10
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rows 10
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a-cols 2 ;; tree 1 fruiting = 2/10
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b-rows 2] ;; tree 2 fruiting = 2/10
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(into
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^:kind/hiccup
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[:svg {:viewBox "0 0 300 180" :width "100%" :style {:background "#ffffff"}}
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[:text {:x 130 :y 16 :text-anchor "middle" :font-size 14 :font-weight 700 :fill "#111827"}
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"AND is an intersection of outcomes"]
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[:text {:x 20 :y 97 :transform "rotate(-90 20 97)" :font-size 9 :fill "#374151"}
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"Tree2 fruiting"]
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[:text {:x 93 :y 172 :text-anchor "middle" :font-size 9 :fill "#374151"}
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"Tree1 fruiting"]]
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(concat
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(for [r (range rows)
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c (range cols)
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:let [x (+ pad (* c cell))
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y (+ 38 (* r cell))
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in-a? (< c a-cols)
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in-b? (< r b-rows)
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fill (cond
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(and in-a? in-b?) "#84cc16" ;; A and B
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in-a? "#dbeafe" ;; A only
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in-b? "#fef3c7" ;; B only
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:else "#f3f4f6")
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stroke (if (and in-a? in-b?) "#4d7c0f" "#9ca3af")]]
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[:rect {:x x :y y :width 10 :height 10 :rx 1.5 :fill fill :stroke stroke}])
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[[:rect {:x 186 :y 146 :width 98 :height 20 :rx 4 :fill "#ecfccb" :stroke "#84cc16"}]
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[:text {:x 235 :y 159 :text-anchor "middle" :font-size 9 :fill "#365314"}
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"A and B = 4/100"]])))
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;; If each tree has fruit chance $2/10$ (0.2), then
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;; $P(\text{tree1 fruiting AND tree2 fruiting}) = 0.2 \times 0.2 = 0.04$ (4%).
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;; {{< pagebreak >}}
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;; ## The OR Rule
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;; $P(A \text{ or } B) = P(A) + P(B)$
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;; It's a new day! Time to collect more fruit.
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;; A tree can be a coconut tree or a bananna tree, but not both at once.
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;; When you visit a tree, the type of tree is mutually exclusive.
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^:kindly/hide-code
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(let [coconut? #{1 7}
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banana? #{3 8 9}
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step 22]
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(into
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^:kind/hiccup
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[:svg {:viewBox "0 0 260 98" :width "100%" :style {:background "#ffffff"}}
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[:text {:x 130 :y 16 :text-anchor "middle" :font-size 14 :font-weight 700 :fill "#111827"}
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"Tree Types"]]
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(concat
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(for [i (range 10)
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:let [x (+ 20 (* i step))
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is-coconut? (contains? coconut? i)
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is-banana? (contains? banana? i)
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fill (cond
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is-coconut? "#fef3c7"
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is-banana? "#dbeafe"
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:else "#e5e7eb")
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stroke (cond
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is-coconut? "#d97706"
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is-banana? "#2563eb"
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:else "#9ca3af")
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label (cond
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is-coconut? "C"
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is-banana? "B"
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:else "O")
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text-fill (cond
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is-coconut? "#92400e"
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is-banana? "#1e40af"
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:else "#6b7280")]]
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[:g
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[:rect {:x x :y 32 :width 16 :height 16 :rx 3 :fill fill :stroke stroke}]
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[:text {:x (+ x 8) :y 43 :text-anchor "middle" :font-size 8 :fill text-fill}
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label]])
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[[:text {:x 58 :y 68 :text-anchor "middle" :font-size 8 :fill "#92400e"}
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"Coconut = 2/10"]
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[:text {:x 132 :y 68 :text-anchor "middle" :font-size 8 :fill "#1e40af"}
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"Banana = 3/10"]
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[:text {:x 208 :y 68 :text-anchor "middle" :font-size 8 :fill "#6b7280"}
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"Other = 5/10"]
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[:text {:x 130 :y 86 :text-anchor "middle" :font-size 9 :fill "#365314"}
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"Coconut or Banana = 5/10"]])))
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;; A tree cannot be both types at once, so just add the probabilities.
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;; $P(\text{coconut or banana}) = \frac{2}{10} + \frac{3}{10} = \frac{5}{10} = 0.5$.
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;; If categories can overlap, adding $P(A)$ and $P(B)$ counts shared cases twice.
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;; Subtract the overlap once to fix that double-counting.
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;; Use $P(A \text{ or } B)=P(A)+P(B)-P(A \text{ and } B)$.
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;; tall or fruiting = tall + fruiting - tall and fruiting.
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;; {{< pagebreak >}}
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;; ## The NOT Rule
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;; $P(\text{not } E) = 1 - P(E)$
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;; Night is coming; you need to find at least one fruit.
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;; If you visit 3 trees with $P(fruit)=\frac{2}{10}$, what is the chance you get at least one fruit?
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;; Use the NOT rule when the event you want is hard to count, but its opposite is easy.
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^:kindly/hide-code
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^:kind/hiccup
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[:svg {:viewBox "0 0 520 190" :width "100%" :style {:background "#ffffff"}}
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[:text {:x 260 :y 16 :text-anchor "middle" :font-size 12 :font-weight 700 :fill "#111827"}
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"Solve the Easier Problem"]
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[:circle {:cx 40 :cy 95 :r 14 :fill "#0f766e"}]
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[:text {:x 40 :y 99 :text-anchor "middle" :font-size 8 :fill "white"} "V1"]
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[:circle {:cx 140 :cy 60 :r 12 :fill "#2563eb"}]
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[:text {:x 140 :y 64 :text-anchor "middle" :font-size 8 :fill "white"} "N"]
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[:circle {:cx 140 :cy 130 :r 12 :fill "#f59e0b"}]
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[:text {:x 140 :y 134 :text-anchor "middle" :font-size 8 :fill "#111827"} "F"]
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[:circle {:cx 240 :cy 35 :r 11 :fill "#2563eb"}]
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[:text {:x 240 :y 39 :text-anchor "middle" :font-size 7 :fill "white"} "NN"]
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[:circle {:cx 240 :cy 75 :r 11 :fill "#f59e0b"}]
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[:text {:x 240 :y 79 :text-anchor "middle" :font-size 7 :fill "#111827"} "NF"]
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[:circle {:cx 240 :cy 115 :r 11 :fill "#f59e0b"}]
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[:text {:x 240 :y 119 :text-anchor "middle" :font-size 7 :fill "#111827"} "FN"]
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[:circle {:cx 240 :cy 155 :r 11 :fill "#f59e0b"}]
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[:text {:x 240 :y 159 :text-anchor "middle" :font-size 7 :fill "#111827"} "FF"]
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[:line {:x1 52 :y1 90 :x2 128 :y2 65 :stroke "#2563eb" :stroke-width 1.8}]
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[:line {:x1 52 :y1 100 :x2 128 :y2 125 :stroke "#d97706" :stroke-width 1.8}]
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[:line {:x1 151 :y1 55 :x2 229 :y2 38 :stroke "#2563eb" :stroke-width 1.6}]
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[:line {:x1 151 :y1 65 :x2 229 :y2 72 :stroke "#d97706" :stroke-width 1.6}]
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[:line {:x1 151 :y1 125 :x2 229 :y2 118 :stroke "#d97706" :stroke-width 1.6}]
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[:line {:x1 151 :y1 135 :x2 229 :y2 152 :stroke "#d97706" :stroke-width 1.6}]
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[:line {:x1 251 :y1 30 :x2 336 :y2 22 :stroke "#2563eb" :stroke-width 1.4}]
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[:line {:x1 251 :y1 40 :x2 336 :y2 42 :stroke "#d97706" :stroke-width 1.4}]
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[:line {:x1 251 :y1 70 :x2 336 :y2 62 :stroke "#d97706" :stroke-width 1.4}]
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[:line {:x1 251 :y1 80 :x2 336 :y2 82 :stroke "#d97706" :stroke-width 1.4}]
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[:line {:x1 251 :y1 110 :x2 336 :y2 102 :stroke "#d97706" :stroke-width 1.4}]
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[:line {:x1 251 :y1 120 :x2 336 :y2 122 :stroke "#d97706" :stroke-width 1.4}]
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[:line {:x1 251 :y1 150 :x2 336 :y2 142 :stroke "#d97706" :stroke-width 1.4}]
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[:line {:x1 251 :y1 160 :x2 336 :y2 162 :stroke "#d97706" :stroke-width 1.4}]
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[:rect {:x 336 :y 16 :width 48 :height 12 :rx 3 :fill "#dbeafe" :stroke "#2563eb"}]
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[:text {:x 360 :y 24 :text-anchor "middle" :font-size 7 :fill "#1e40af"} "NNN"]
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[:rect {:x 336 :y 36 :width 48 :height 12 :rx 3 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 360 :y 44 :text-anchor "middle" :font-size 7 :fill "#92400e"} "NNF"]
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[:rect {:x 336 :y 56 :width 48 :height 12 :rx 3 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 360 :y 64 :text-anchor "middle" :font-size 7 :fill "#92400e"} "NFN"]
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[:rect {:x 336 :y 76 :width 48 :height 12 :rx 3 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 360 :y 84 :text-anchor "middle" :font-size 7 :fill "#92400e"} "NFF"]
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[:rect {:x 336 :y 96 :width 48 :height 12 :rx 3 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 360 :y 104 :text-anchor "middle" :font-size 7 :fill "#92400e"} "FNN"]
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[:rect {:x 336 :y 116 :width 48 :height 12 :rx 3 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 360 :y 124 :text-anchor "middle" :font-size 7 :fill "#92400e"} "FNF"]
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[:rect {:x 336 :y 136 :width 48 :height 12 :rx 3 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 360 :y 144 :text-anchor "middle" :font-size 7 :fill "#92400e"} "FFN"]
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[:rect {:x 336 :y 156 :width 48 :height 12 :rx 3 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 360 :y 164 :text-anchor "middle" :font-size 7 :fill "#92400e"} "FFF"]
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[:rect {:x 420 :y 26 :width 90 :height 16 :rx 4 :fill "#dbeafe" :stroke "#2563eb"}]
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[:text {:x 465 :y 37 :text-anchor "middle" :font-size 8 :fill "#1e40af"} "No fruit: NNN"]
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[:rect {:x 420 :y 50 :width 90 :height 16 :rx 4 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 465 :y 61 :text-anchor "middle" :font-size 8 :fill "#92400e"} "Has fruit: 7 paths"]]
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;; $P(not fruit) = 1 - \frac{2}{10} = \frac{8}{10}$
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;; $P(\text{no fruit in 3 trees}) = \frac{8}{10}\times\frac{8}{10}\times\frac{8}{10} = 0.512$.
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;; Invert back to the original question:
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;; $P(\text{at least one fruit}) = 1 - 0.512 = 0.488$.
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;; {{< pagebreak >}}
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;; ## The "Given That" Rule
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;; $P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)}$
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;; The bar symbol $|$ means "given".
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;; Dark clouds move in, so your wood-gathering plan must adapt to the weather you actually get.
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;; Question prompt us to gather new statistics and probabilities.
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^:kindly/hide-code
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^:kind/hiccup
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[:svg {:viewBox "0 0 560 300" :width "100%" :style {:background "#ffffff"}}
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[:text {:x 280 :y 22 :text-anchor "middle" :font-size 14 :font-weight 700 :fill "#111827"}
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"Island weather affects finding dry wood"]
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[:circle {:cx 70 :cy 150 :r 22 :fill "#0f766e"}]
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[:text {:x 70 :y 155 :text-anchor "middle" :font-size 10 :fill "white"} "All (100)"]
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[:line {:x1 92 :y1 140 :x2 175 :y2 90 :stroke "#0f766e" :stroke-width 2}]
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[:line {:x1 92 :y1 160 :x2 175 :y2 210 :stroke "#0f766e" :stroke-width 2}]
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[:circle {:cx 195 :cy 85 :r 22 :fill "#2563eb"}]
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[:text {:x 195 :y 84 :text-anchor "middle" :font-size 9 :fill "white"} "Rain"]
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[:text {:x 195 :y 95 :text-anchor "middle" :font-size 9 :fill "white"} "(40)"]
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[:circle {:cx 195 :cy 215 :r 22 :fill "#f59e0b"}]
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[:text {:x 195 :y 214 :text-anchor "middle" :font-size 8 :fill "#111827"} "Not Rain"]
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[:text {:x 195 :y 224 :text-anchor "middle" :font-size 8 :fill "#111827"} "(60)"]
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[:line {:x1 217 :y1 77 :x2 320 :y2 55 :stroke "#2563eb" :stroke-width 2}]
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[:line {:x1 217 :y1 93 :x2 320 :y2 115 :stroke "#2563eb" :stroke-width 2}]
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[:line {:x1 217 :y1 207 :x2 320 :y2 185 :stroke "#d97706" :stroke-width 2}]
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[:line {:x1 217 :y1 223 :x2 320 :y2 245 :stroke "#d97706" :stroke-width 2}]
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[:rect {:x 308 :y 35 :width 112 :height 30 :rx 6 :fill "#fef3c7" :stroke "#2563eb"}]
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[:text {:x 364 :y 54 :text-anchor "middle" :font-size 9 :fill "#92400e"} "Dry | Rain (8)"]
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[:rect {:x 308 :y 95 :width 112 :height 30 :rx 6 :fill "#dbeafe" :stroke "#2563eb"}]
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[:text {:x 364 :y 114 :text-anchor "middle" :font-size 9 :fill "#1e40af"} "Not Dry | Rain (32)"]
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[:rect {:x 308 :y 165 :width 112 :height 30 :rx 6 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 364 :y 184 :text-anchor "middle" :font-size 9 :fill "#92400e"} "Dry | Not Rain (54)"]
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[:rect {:x 308 :y 225 :width 112 :height 30 :rx 6 :fill "#dbeafe" :stroke "#d97706"}]
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[:text {:x 364 :y 244 :text-anchor "middle" :font-size 9 :fill "#1e40af"} "Not Dry | Not Rain (6)"]
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[:line {:x1 420 :y1 50 :x2 478 :y2 110 :stroke "#d97706" :stroke-width 1.5 :stroke-dasharray "4 3"}]
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[:line {:x1 420 :y1 180 :x2 478 :y2 110 :stroke "#d97706" :stroke-width 1.5 :stroke-dasharray "4 3"}]
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[:line {:x1 420 :y1 110 :x2 478 :y2 210 :stroke "#60a5fa" :stroke-width 1.5 :stroke-dasharray "4 3"}]
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[:line {:x1 420 :y1 240 :x2 478 :y2 210 :stroke "#60a5fa" :stroke-width 1.5 :stroke-dasharray "4 3"}]
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[:circle {:cx 500 :cy 110 :r 22 :fill "#fef3c7" :stroke "#d97706"}]
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[:text {:x 500 :y 107 :text-anchor "middle" :font-size 8 :fill "#92400e"} "Dry"]
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[:text {:x 500 :y 117 :text-anchor "middle" :font-size 8 :fill "#92400e"} "(62)"]
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[:circle {:cx 500 :cy 210 :r 22 :fill "#dbeafe" :stroke "#2563eb"}]
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[:text {:x 500 :y 207 :text-anchor "middle" :font-size 7 :fill "#1e40af"} "Not Dry"]
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[:text {:x 500 :y 217 :text-anchor "middle" :font-size 8 :fill "#1e40af"} "(38)"]]
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;; Probability is about identifying the interesting set of outcomes.
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;; A tree helps you enumerate and count interesting and possible outcomes.
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;; For "dry wood given rain," count within rainy outcomes: $8/40$.
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;; For "rain given dry wood," count within dry outcomes (all yellow): $8/62$.
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;; It's a matter of filtering to cases where the condition is true, then count outcomes inside that filtered group.
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;; {{< pagebreak >}}
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;; ## Distribution Matters
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;; Where will you camp?
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;; Continuous variables like temperature can be any value.
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;; Observations rarely spread evenly; instead, they cluster and vary.
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;; Island A and Island B both average 75°F, yet Island A is highly predictable (72°F to 78°F) while Island B is highly volatile (30°F to 120°F).
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;; To truly understand the situation, we must see the distribution, the shape of the data.
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;; ::: {layout-ncol=2}
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^:kindly/hide-code
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(-> [{:temperature "30-44F" :days 0}
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{:temperature "45-59F" :days 0}
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{:temperature "60-74F" :days 38}
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{:temperature "75-89F" :days 62}
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{:temperature "90-104F" :days 0}
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{:temperature "105-119F" :days 0}
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{:temperature "120-134F" :days 0}]
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(pj/lay-value-bar :temperature :days)
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(pj/options {:title "Island A"}))
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^:kindly/hide-code
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(-> [{:temperature "30-44F" :days 2}
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{:temperature "45-59F" :days 4}
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{:temperature "60-74F" :days 8}
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{:temperature "75-89F" :days 10}
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{:temperature "90-104F" :days 7}
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{:temperature "105-119F" :days 4}
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{:temperature "120-134F" :days 2}]
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(pj/lay-value-bar :temperature :days)
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(pj/options {:title "Island B"}))
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;; :::
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;; A distribution reveals where observations cluster and how frequently they occur.
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;; Variance quantifies this spread by measuring the average squared distance from the mean.
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;; A wider spread generally implies higher variance, but the exact value depends on the range and the shape of the distribution.
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;; {{< pagebreak >}}
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;; ## Survival Quiz
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;; ![](coconut.svg){width="50%" fig-align="center"}
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;; Time to try to use your radio to contact help.
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;; a. Your radio has a $\frac{2}{3}$ failure rate. What is the probability that your signal is successful?
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;; b. Finding fruit and using the radio are independent events. If fruit is found $\frac{2}{10}$ of the time and the radio works $\frac{1}{3}$ of the time, what is the probability that both happen?
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;; c. Rainfall data shows most days have 0 mm of rain, but one rare day has a 600 mm flood. How would you describe the shape of this distribution?
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;; d. Land Area A has a height standard deviation of 2 ft (very flat). Land Area B has a height standard deviation of 80 ft (very rugged). Which area is more likely to contain a mountain peak?

‎src/math/stats/quantquestions/what_are_the_odds/cheat_zine.png‎

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