Among travelers arriving at a small airport, 80% ?y on major airlines and 20% ?y

Question

Among travelers arriving at a small airport, 80% ?y on major airlines and 20% ?y on
privately owned planes. Of those traveling on major airlines, 50% travel for business reasons, whereas 70% arriving privately owned planes travel for business reasons. Suppose that we randomly select one person arriving at airport. What is the probability that the person is traveling on business? What is the probability the person is traveling on business on a privately owned plan? What is the probability that the person will take a ma jor airline given that the person travels on business?

Explanation / Answer

Given P(major)=0.8 --- P(business given major)=0.5 P(owned)=0.2----P(business given owned)=0.7 ------------------------------------------------------------------------------ What is the probability that the person is traveling on business? 0.8*0.5 + 0.2*0.7 =0.54 ------------------------------------------------------------------------------ What is the probability the person is traveling on business on a privately owned plan? 0.2*0.7 = 0.14 ----------------------------------------------------------------------------------------- What is the probability that the person will take a major airline given that the person travels on business? 0.8*0.5/0.54 =0.7407

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