Question

The probability that an international flight leaving the United States is delayed in departing (event D) is .29. The probability that an international flight leaving the United States is a transpacific flight (event P) is .59. The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .11. (a) What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight

Answer 1

`P(D|P)= (0.11)/(0.59)=0.186`

Explanation:

For this case we have defined the following events:

D= "An international flight leaving the United States is delayed in departing"

P="An international flight leaving the United States is a transpacific flight "

And we have defined the probabilities:

`P(D)= 0.29 , P(P) = 0.59`

And for the event: "an international flight leaving the U.S. is a transpacific flight and is delayed in departing"
`D \cap P` we know the probability:

`P(D \cap P) =0.11`

We want to find this probability:

What is the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight

So we want this probability:

`P(D|P)`

And we can use the conditional formula from the Bayes theorem given two events A and B:

`P(A|B) = (P(A \cap B))/(P(B))`

And if we use this formula for our case we have:

`P(D|P)= (P(D \cap P))/(P(P))`

And if we replace the values we got:

`P(D|P)= (0.11)/(0.59)=0.186`