Discrrete mathematics for computer science proability 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

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)

• 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