The probability that an international flight leaving the United States is delayed in departing (event $D$ ) is.35. The probability that an international flight leaving the United States is a transpacific flight (event $P$ ) is .40 . The probability that an international flight leaving the U.S. is a transpacific flight and is delayed in departing is .14 .
(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? (Round your answer to 4 decimal places.)
Probability
Answer
Final Answer: The probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight is \(\boxed{0.35}\).
Step 1 ：The problem is asking for the conditional probability of an event. Specifically, we are asked to find the probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight. This is denoted as \(P(D|P)\).
Step 2 ：The formula for conditional probability is \(P(A|B) = P(A \cap B) / P(B)\). In this case, \(A\) is the event that the flight is delayed (\(D\)) and \(B\) is the event that the flight is a transpacific flight (\(P\)). We are given \(P(D \cap P) = 0.14\) and \(P(P) = 0.40\).
Step 3 ：We can substitute these values into the formula to find the answer: \(P(D|P) = P(D \cap P) / P(P) = 0.14 / 0.40 = 0.35\).
Step 4 ：Final Answer: The probability that an international flight leaving the United States is delayed in departing given that the flight is a transpacific flight is \(\boxed{0.35}\).
