Question

Problem 2-11 (Algorithmic) Let A be an event that a person's primary method of transportation to and from work is an automobile and B be an event that a person's primary method of transportation to and from work is a bus. Suppose that in a large city P(A) = 0.48 and P(B) = 0.32. Are events A and B mutually exclusive? Yes What is the probability that a person uses an automobile or a bus in going to and from work? If required, round your answer to two decimal places. Find the probability that a person’s primary method of transportation is some means other than a bus. If required, round your answer to two decimal places. P(Bc) =

Answer 1

The events are mutually exclusive, because your primary method can't be both a driving a car or taking a bus.

Since they are exclusive, the probability of the "or" clause is the sum of the probabilities:

$P(A\lor B)=P(A)+P(B)=0.48+0.32=0.8$

Since a person primarily takes a bus with probability 0.32, the opposite happens with probability

$1-P(B) = 1-0.32=0.68$