Workout this question.The probability that a regularly scheduled flight departs on time is PD) = 0.83; the
probability that it arrives on time is P(A) =0.82; and the probability that it departs and arrives on
time is PDA) = 0.78. Find the probability that a plane (a) arrives on time, given that it departed
on time, and (b) departed on time, given that it has arrived on time.
To find the probability that a plane arrives on time, given that it departed on time, we can use the conditional probability formula:
P(A|D) = P(DA) / P(D)
Given that P(DA) = 0.78 and P(D) = 0.83, we can calculate:
P(A|D) = 0.78 / 0.83 ≈ 0.94
Therefore, the probability that a plane arrives on time, given that it departed on time, is approximately 0.94.
To find the probability that a plane departed on time, given that it has arrived on time, we can also use the conditional probability formula:
P(D|A) = P(DA) / P(A)
Given that P(DA) = 0.78 and P(A) = 0.82, we can calculate:
P(D|A) = 0.78 / 0.82 ≈ 0.95
Therefore, the probability that a plane departed on time, given that it has arrived on time, is approximately 0.95.