According to exit polls from the 2000 presidential election, the probability of a voter self-identifying as gay (including lesbians) was P(G) 0.04. The probability of voting for Bush, given that a voter was gay, was P(B given G) 0.25, and the probability of voting for Bush, given that a voter was not gay, was P(B given not G) 0.50.
a. Find P(G and B), the probability of being gay and voting for Bush.
b. Find P(not G and B), the probability of not being gay and voting for Bush.
c. Note that a minority of voters were gay. Would we expect P(B) to be closer to P(B given G) 0.25 or to P(given not G) 0.50?
d. Find P(B), the overall probability of voting for Bush, keeping in mind that a voter was either gay and voted for Bush or not gay and voted for Bush.
e. Use the definition of conditional probability and your answers to parts (a) and (d) to find P(G given B), the probability of being gay given that a voter voted for Bush.