Question

A survey on travelers arriving at an airport revealed that 60% fly on major airlines, 30% fly on privately owned planes, and the remainder 10% fly on commercially owned planes. Of those traveling on major airlines, 50% are traveling for business reasons, whereas of those arriving on private planes, 60% are traveling for business reasons. Finally, of those arriving on other commercially owned planes, 90% are traveling for business reasons. Suppose that we randomly select one person arriving at this airport. What is the probability that the person

(a) is traveling for business?

(b) is traveling for business and on a privately owned plane?

(c) arrived on privately owned plane, given that the person is traveling for business reasons?

Answer 1

a) P(Travelling for business) = 0.60*0.50 + 0.30*0.60 + 0.10*0.90 = 0.57

b) P(Travelling for business and privately owned plane) = 0.30*0.60 = 0.18

c) P(Privately owned plane | Travelling for Business) = 0.18/0.57 = 0.3158