Question

Of of the travelers arriving at a small airport, 60% fly on majorairlines, 30% fly on privately owned airlines, and the remainder fly on commer-cially owned planes not belonging to a major airline. Of those traveling on majorairlines, 50% are traveling for business, whereas 60% of those arrving on privateplanes are traveling for business and 90% arriving on other commercially ownedplanes are traveling for business reasons. Suppose that we randomly select oneperson arriving at this airport. What is the probability that the person is traveling on business?

Answer 1

Answer:

the probability that the person is traveling on business is 0.57

Step-by-step explanation:

First we need to define our events:

E₁ = person flies on major airlines

E₂ = person flies on private airlines.

E₃ = person flies on planes not belonging to a major airline.

Then, our probabilities are:

P(E₁) = .60

P(E₂) =.30

P(E₃) = 0.1

But then the problem gives us one more event, the event of traveling for business.

If we call B to the event of travelling for business we get that:

• P(traveling for business given that they are flying in major airlines) = P(B|E₁) =.50

• P(traveling for business given that they are flying on private airlines) = P(B|E₂) =.60

• P(traveling for business given that they are flying on commercial planes not belonging to major airlines) = P(B|E₁) =.90

The problem asks us to find the probability that the person is traveling on business (P(B)).

Since we have conditional probabilities, we need to use the Law of Total Probability:

P(B) = P(B|E₁)P(E₁) + P(B|E₂)P(E₂) + P(B|E₃)P(E₃)

P(B) = (.5)(.6) + (.6)(.3) + (.9)(.1) = .30 +.18 + .09 = 0.57

Therefore, the probability that the person is traveling on business is 0.57