A survey of magazine subscribers showed that 45.5% rented a car during the past

Question

A survey of magazine subscribers showed that 45.5% rented a car during the past 12 months for business reasons, 58% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons. Round your answers to three decimal places. 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?

Explanation / Answer

P( business reasons) = 0.455, P( Personal reasons) = 0.58

P( Both business and personal reasons) = 0.30

a)

P( business or personal reasons) = ?

Using conditional probability formula, p(A or B) = P(A) + P(B) - P( A and B)

P( business or personal reasons) = P( Business reason) + P( Personal reasons)

- P( business and personal reasons)

= 0.455 + 0.58 - 0.30

= 0.735

P( business or personal reasons) = 0.735

b)

P(Did not rent car for either business or personal reasons) = P(Neither Business of personal reasons)

= 1 - P( business or personal reasons)

= 1 - 0.735

= 0.265

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.