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the probability that an international flight leaving the united states is delayed in departing (event d) is .36. the probability that an international flight leaving the united states is a transpacific flight (event p) is .25. the probability that an international flight leaving the u.s. is a transpacific and is delayed in departing is .09. What is the probability that an international flight leaving the United States is delayed given that the flight is a transpacific flight?

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Edufirst

Answer:

                     [tex]\large\boxed{\large\boxed{0.36}}[/tex]

Explanation:

This is a typical problem of conditional probability.

In this case you know:

  • the probability of the event D (an international flight leaving the U.S. is delayed in departing), which is 0.36 and you can write as P(D) = 0.36

  • the probability of event P (an international flight leaving the U.S.  is a transpacific flight), which is 0.25 and you can write as P(P) = 0.25;

  • the joint probability of event P and D (international flight leaving the U.S. is a transpacific and is delayed in departing), which is 0.09 and you can write as P (P ∩ D) = 0.09.

You need to determine the probability that an international flight leaving the United States is delayed given that the flight is a transpacific flight, i.e. the conditional probability P (D/P).

Hence, use the formula for conditional probability:

  • P (D/P) = P (D ∩ P) / P(D) = P (P ∩ D) / P (D)

  • P (D/P) = 0.09 / 0.25 = 0.36