warmup

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Probability Warmup
Estimating the answer to an
embarrassing question
To estimate what percentage of a group has
property P, ask each member of the group
to flip a coin and raise a hand if the flip is
heads (H) or the individual has P
Assumptions:
H and P are independent
¬P is not embarrassing
Everyone answers honestly
Calculating Pr(P) from Pr(H∪P)
H
P
• Because H and P are independent events,
Pr(H∩P) = Pr(H) ∙ Pr(P).
• Pr(H) = .5
• Pr(H∪P) = Pr(H) + Pr(P) - Pr(H∩P).
• So Pr(P) = Pr(H∪P) - Pr(H) + Pr(H)∙Pr(P)
• Pr(P) = 2 ∙ Pr(H∪P) – 1
FINIS

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