According to exit polls from the 2000 presidential election, the probability of a voter supporting stricter gun control laws was P(C) 0.60. The probability of voting for Bush, given that a voter supported stricter gun control laws, was P(B given C) 0.34, and the probability of voting for Bush, given that a voter did not support stricter gun control laws, was P(B given not C) 0.74.
a. Find P(C and B), the probability of supporting stricter gun control laws and voting for Bush.
b. Find P(not C and B), the probability of not supporting stricter gun control laws and voting for Bush.
c. Note that a majority of voters supported stricter gun control laws. Would we expect P(B) to be closer to P(B given C) 0.34 or to P(B given not C) 0.74?
d. Find P(B), the overall probability of voting for Bush, keeping in mind that a voter either supported gun control and voted for Bush or did not support gun control and voted for Bush.
e. Use the definition of conditional probability and your answers to parts (a) and (d) to find P(C given B), the probability of supporting stricter gun control laws, given that a voter voted for Bush.
f. Compare P(C) and P(C given B), and discuss why they are quite different. 6.