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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:

A) Write your data using mathematical (probabilities) language:

1. The probability that an international flight leaving the united states is delayed in departing (event d) is .36.

  • P(D) = 0.36

2. The probability that an international flight leaving the united states is a transpacific flight (event p) is .25.

  • P(P) = 0.25

3. The probability that an international flight leaving the u.s. is a transpacific and is delayed in departing is .09.

  • P(D∩P) = 0.09; note that P(D∩P) is, by definition, equal to P(P∩D)

4. What is the probability that an international flight leaving the United States is delayed given that the flight is a transpacific flight?

  • P(D/P) = ?

B) Solve:

Note that the two events, P and D, are independent because the product of their probabilities is equal to the joint probability:

  • P(P) × P(D) = 0.36 × 0.25 = 0.09 = P (P∩D)

Those, given that the two events are independent the probability of the event D does not change by knowing the probability of the event P, and you shall have the:

  • the probability that an international flight leaving the United States is delayed given that the flight is a transpacific flight is the same as  the probability that an international flight leaving the united states is delayed in departing, which is 0.36.

When you apply the conditional probability formula you prove it:

  • Conditional probability formula: P (A/B) = P (A ∩ B) / P(B)

  • In our case of the flights: P (D/P) = P (D ∩ P) / P (P) = 0.09/0.25 = 0.36, such as we expected.