Question

Of the travelers arriving at a small airport, 50% fly on major airlines, 20% fly on privately owned planes, and the remainder fly on commercially owned planes not belonging to a major airline. Of those traveling on major airlines, 40% are traveling for business reasons, whereas 60% of those arriving on private planes and 90% of those arriving on other commercially owned planes are traveling for business reasons. Suppose that we randomly select one person arriving at this airport.(a) What is the probability that the person is traveling on business?(b) What is the probability that the person is traveling for business on a privately owned plane?(c) What is the probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons? (Round your answers to four decimal places.)(d) What is the probability that the person is traveling on business, given that the person is flying on a commercially owned plane?

Answer 1

The probability that the person is traveling on business is 0.59

The probability that the person is traveling for business on a privately owned plane is 0.12

The probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons is 0.12

The probability that the person is traveling on business, given that the person is flying on a commercially owned plane is 0.27

Explanation:

50% fly on major airlines, Of those , 40% are traveling for business reasons

20% fly on privately owned planes, 60% are traveling for business reasons

30% (the remainder) fly on commercially owned planes, 90% are traveling for business reasons

(a) What is the probability that the person is traveling on business?

To get the probability of people traveling on business we have to know the probability of traveling for business in each possibility.

That will be,

Major airlines= 0.50 x 0.40=0.20

Privately owned planes= 0.20 x 0.60=0.12

Commercially owned planes= 0.30 x 0.90=0.27

The probability that the person is traveling on business=0.20+0.12+0.27=0.59

(b) What is the probability that the person is traveling for business on a privately owned plane?

That will be the probability of flying in a privately owned plane multiply for the probability of traveling for business

= 0.20 x 0.60=0.12

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

= 0.20 x 0.60=0.12

(d) What is the probability that the person is traveling on business, given that the person is flying on a commercially owned plane?

= 0.30 x 0.90=0.27