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Of the travelers arriving at a small airport, 50% fly on major airlines, 20% fly on...

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Basic Math

Of the travelers arriving at a small airport, 50% fly on majorairlines, 20% fly on privately owned planes, and the remainder flyon commercially owned planes not belonging to a major airline. Ofthose traveling on major airlines, 40% are traveling for businessreasons, whereas 60% of those arriving on private planes and 90% ofthose arriving on other commercially owned planes are traveling forbusiness reasons. Suppose that we randomly select one personarriving at this airport.

(a) What is the probability that the person is traveling onbusiness?

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

(c) What is the probability that the person arrived on aprivately owned plane, given that the person is traveling forbusiness reasons? (Round your answers to four decimal places.)

(d) What is the probability that the person is traveling onbusiness, given that the person is flying on a commercially ownedplane?

Answer & Explanation Solved by verified expert
4.4 Ratings (808 Votes)

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
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