## MAT 131 Sample Quiz 10

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 illustrating the survey results.

2. Find the probability that a voter selected at random is from Philadelphia and prefers
the Republican candidate.

3. Find the probability that a voter selected at random prefers the Republican candidate.

4. Find the probability that a voter selected at random is from Philadelphia, given that
the voter prefers a Democratic candidate.

Answers