A pollster is hired by a presidential candidate to determine his support among the voters of Pennsylvania's two big cities: Philadelphia and Pittsburgh. The pollster uses the following sampling technique: Select one of the cities at random and then poll a randomly selected voter from that city. Suppose that two-fifths of the voters in Philadelphia prefer the Republican candidate and three-fifths prefer the Democratic candidate and that in Pittsburgh, two-thirds of the voters prefer the Republican candidate and one-third prefer the Democratic candidate.
1. Draw a tree diagram describing the survey.
2. Find the probability that a voter selected at random is from Philadelphia and prefers the Republican candidate.
The probability is 2/10 = 1/5 = 0.200
3. Find the probability that a voter selected at random prefers the Republican candidate.
The probability is 2/10 + 2/6 = 6/30 + 10/30 = 16/30 = 8/15 ≈ 0.533
4. Find the probability that a voter selected at random is from Philadelphia, given that the voter prefers a Democratic candidate.
