Question

According to exit polls from the 2000 presidential election, the probability of a voter self-identifying as homosexual (including lesbians) was P(G) = 0.04. The probability of voting for Bush, given that a voter was homosexual, was P(B given G) = 0.25, and the probability of voting for Bush, given that a voter was not homosexual, was P(B given not G) = 0.50.

a) Find P(G and B), the probability of being homosexual and voting for bush.

b) Find P(not G and B), the probability of not being homosexual and voting for bush.

c) Note that a minority of voters were homosexual. Would you expect P(B) to be closer to P(B given G) = 0.25, or P(given not G) = 0.50

d) Fine P(B), the probability of voting for bush, keeping in mind that a voter is either homosexual and voted for Bush or not homosexual and voted for Bush.

e) Using the definition of conditional probability and your answers to part (a) and (d), to find P(G given B), the probability of being homosexual given that a voter voted for Bush

Answer 1

Given

a) The probability of being homosexual and voting for bush

b) Now,

The probability of not being homosexual and voting for bush

c) P(G ) is very small, then we can expect P(B) to closer to P(B given not G)

d) P(B) = 0.49

e)