#set document(title: "4.8 Chapter 4 Formulas", author: "Rachel Webb")
#set page(width: 8.5in, height: auto, margin: 1in)
#import "@preview/cetz:0.5.2"
#set text(font: ("STIX Two Text", "Libertinus Serif", "New Computer Modern"), size: 10.5pt, lang: "en")
#show math.equation: set text(font: ("STIX Two Math", "New Computer Modern Math"))
#set par(justify: true, leading: 0.62em, spacing: 0.9em)
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#set list(spacing: 1.1em)
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#let BLUE = rgb("#183B6F")     // brand navy — section bars + example/solution labels (white on navy 11.09:1)
#let ORANGE = rgb("#A94509")   // brand primary-700 — AA-safe deep orange for TEXT (5.93:1 on white; raw brand #F37021 is 2.94:1 and must never carry text)
#let RED = rgb("#DC2626")      // brand error-600
#let GREEN = rgb("#059669")    // brand success-600 (decoration only; small green text uses green-text #007942)

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#show heading.where(level: 4): it => text(fill: BLUE, weight: "bold", size: 10.5pt, it.body)

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#let solutionbox(body) = block(above: 4pt, below: 8pt)[
  #text(fill: BLUE, weight: "bold", size: 8.5pt)[Solution] #linebreak() #body]

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// Standardize inlined figure sizes: measure the natural CeTZ canvas, then scale to a
// consistent envelope (aspect-aware; see build_typst.py FIG_* constants). Unlike the
// print preamble, dimensions are FLOORED: in an editor a user can trim a figure to a
// degenerate 1-D shape (a bare line), and w/h or tw/w would then divide by zero.
#let _STD_W = 3.5
#let _WIDE_W = 5.6
#let _MAX_H = 3.4
#let _ASPECT_WIDE = 2.2
#let _UPSCALE_MAX = 1.15
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}

#show figure: set block(breakable: false)
#set figure(gap: 8pt)
#show figure.caption: set text(size: 8.5pt, fill: rgb("#555"))


    
== 4.8#h(0.6em)Chapter 4 Formulas


    #figure(table(
  columns: 2, align: left, inset: 6pt,
  table.header([#strong[Complement Rules:] P(A) + P(A#super[C]) = 1

            P(A) = 1 – P(A#super[C])

            P(A#super[C]) = 1 – P(A)], [#strong[Mutually Exclusive Events:] P(A ∩ B) = 0]),
  [#strong[Union Rule:] P(A U B) = P(A) + P(B) – P(A ∩ B)], [#strong[Independent Events:] P(A ∩ B) = P(A) ‧ P(B)],
  [#strong[Intersection Rule:] P(A ∩ B) = P(A) ‧ P(B|A)], [#strong[Conditional Probability Rule:] #math.equation(block: false, alt: "P open parenthesis A ∣ B close parenthesis equals the fraction P open parenthesis A intersection B close parenthesis over P open parenthesis B close parenthesis")[$P ( A ∣ B ) = frac(P ( A ∩ B ), P ( B ))$]],
  [#strong[Fundamental Counting Rule:] m#sub[1]·m#sub[2]···m#sub[n]], [#strong[Factorial Rule:] n! = n·(n – 1)·(n – 2)···3·2·1],
  [#strong[Combination Rule:] #math.equation(block: false, alt: "n C sub r equals the fraction n ! over open parenthesis r ! open parenthesis n minus r close parenthesis ! close parenthesis")[$n C_(r) = frac(n !, ( r ! ( n − r ) ! ))$]], [#strong[Permutation Rule:] #math.equation(block: false, alt: "n P sub r equals the fraction n ! over open parenthesis n minus r close parenthesis !")[$n P_(r) = frac(n !, ( n − r ) !)$]],
))