Question

The probability that a regular-scheduled flight departs on time is 0.83, the probability that it arrives on time is 0.82, and the probability that it departs and arrives on time is 0.78. Find the probability that a plane arrives on time given that it departs on time.

Answer 1

To find the probability that a plane arrives on time given that it departs on time, we can use conditional probability. P(A|D) = P(D and A) / P(D) = 0.78 / 0.83 = 0.939, or 93.9%.

Step-by-step explanation:

To find the probability that a plane arrives on time given that it departs on time, we can use conditional probability. Let A represent the event that a plane arrives on time and D represent the event that a plane departs on time. We are given P(D) = 0.83, P(A) = 0.82, and P(D and A) = 0.78. The conditional probability of A given D, denoted as P(A|D), can be calculated using the formula P(A|D) = P(D and A) / P(D).

Substituting the given values, we have P(A|D) = 0.78 / 0.83 = 0.939, or 93.9%.