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

From the given data, the following Table is formed:

	Major Airlines	Privately owned planes	Commercially owned planes	Total
Business	0.50X0.40=0.20	0.20X0.60=0.12	0.30X0.90=0.27	0.59
Not business	0.50-0.20=0.30	.20-0.12=0.08	0.30-0.27=0.03	0.41
Total	0.50	0.20	0.30	1.00

(a)
P(Business) = 0.59

(b)

P(Business & Privtely owned plane) = 0.12

(c)
P(Privately owned plane/ Business) = P(Privately owned plane & Business)/P(Business)

                                                     = 0.12/0.59 = 0.2034

(d)

P(Business/ Commercially owned plane)=P(Business & Commerically owned plane)/P(Commercially owned plane)

                                                            = 0.27/0.30 = 0.9