Probablities questions (MATH)
MATH Intro to Math Stat
Instructions: Complete the following. Show all work.
(1) An insurance agency sells various types of insurance policies. 40% of their clients buy auto insurance policies, 30% of their clients buy home insurance policies, and 15% of their clients buy both home and auto insurance policies.
a. Compute the probability a randomly selected client buys a home or auto insurance policy.
b. Compute the probability a randomly selected client does not buy a home insurance policy.
c. Compute the probability a randomly selected client buys neither a home insurance policy nor an auto insurance policy.
d. Compute the probability a randomly selected client buys a home insurance policy but not an auto insurance policy.
(2) Tom has 3 red marbles and 3 white marbles. These are placed into an urn and you pick 2 of them, one after another, replacing the first before choosing the second.
a. What is the probability you pick 1 red marble and 1 white marble?
b. If you pick two marbles of the same color you win $1, and if you don’t you lose $1. What is the probability that you win $1? That you lose $1?