Expert: Sherry Wallin - 3/24/2010

Question
Hello! Hope U R fine..I would really appreciate if u could help me with this question!

A survey showed that:

45% rented car during the past 12 months for business purposes
54% rented a car during the past 12 months for personal reasons
30% rented a car during the past 12 months for both business and personal reasons

A) What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons

B) What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?

I look forward to a positive response..Thanks in Advance :-)

Answer
Hi Bells~
    Let's label your 2 questions as question 1 and question 2. This is a union and intersection type problem. I am assuming for question 1 that this is an exclusive or, meaning that you don't want to include the probability of both renting for business and personal use. Let A = business use and B = personal use (here I am using A and B as sets). So P(A) = .45 and P(B) = .54 and
P(A n B) = .3 from the givens in the problem. What question 1 is asking for is the probability of the intersection of A and B:
P(A U B) = P(A) + P(B) - P(A n B) = .45 + .54 - .3 = .69

For question 2 what they are asking for is the complement of question 1 which is simply
1 - .69 = .31

Math Prof