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# Philosophy XX1 – Chapter 7.docx

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School
Department
Philosophy
Course
PHIL 105
Professor
J.Katz
Semester
Fall

Description
Philosophy XX1 – Chapter 6­7 What is the chance of a blind draw of a non­heart?  39/52 = 3/4 Favourable chances → chance of getting right (i.e. non­heart) Odds are favourable vs unfavourable Chances are favourable vs total number  Fair bet: a bet such that a the probability of winning x the payoff is the same for every player.  Probability 1 → ratio: favourable:total Probability 2 → observed relative frequency  Probability 3 → degree of rational belief  Rules of Probability Pr (h/e) = n  h → hypothesis e → evidence  Rule 1: 0 ≤ n ≤ 1 Rule 2: if evidence entails the hypothesis, then Pr(h/e) = 1  Rule 3 (Sum Rule): disjunctive events  → Pr(h1 or h2/e) = Pr(h1/e) + Pr(h2/e)  ­ must be mutually exclusive (can't overlap)  Rule 4 (Product Rule): conjunctive events → Pr(h1 and h2/e) = Pr(h1/e)*Pr(h2/e)  ­ independent events  Fundamental Theorem → If Pr(h/e) = n then Pr(not h/e) = 1­n  Cost/Payoff Probability x payoff − cost Decision Contexts: 1. Risk ­ Know the probabilities of various outcomes ­ We can assign only probabilities to possible states  2. Certainty ­ We can assign probabilities of 1 or 0  3. Uncertainty  ­ We cannot assign any probability  Decision Matrix Rule: Maximize Expected Utility  Unknown Probabilities:  1. Look for dominant action 2. Look for satisfactory action  Gambler → action that gives possibility of best outcome Cautious → act to avoid worst outcome Calculator → value the preferences  Pascal Law of Averages (Gamblers Fallacy) Chapter 7  Tyc
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