Discrrete mathematics for computer science proability warmup

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) = Pr(H∪P) = Pr(H) + Pr(P) - Pr(H∩P) So Pr(P) = Pr(H∪P) - Pr(H) + Pr(H)∙Pr(P) Pr(P) = ∙ Pr(H∪P) – FINIS