Question
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.
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.
Answers
GPT 3.5
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.
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.