2 years ago
The probability that a regularly scheduled flight departs on time is P (D)=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 P (D ∩ A)=0.78. Find the probability that a plane:
a. arrives on time given that it departed on time
b. departed on time given that it has arrived on time
a. arrives on time given that it departed on time
b. departed on time given that it has arrived on time
1 Answers
Best Answer
esharron Staff answered 2 years ago
esharron Staff answered 2 years ago
Given,
Probability of departing on time P (D)=0.83
Probability of arriving on time P (A)=0.82
Probability of departing and arriving on time P (D ∩ A)=0.78
a) Probability that a plan arrives on time given that it departed on time:
The probability that a plan arrives on time given that it departed on time is calculated as follows:
P (A/D)= probability that the plan arrives on time given that it departed on time
P (A/D)= (P (A ∩ D))/(P (D))
= (0.78)/(0.83)
P (A/D)=0.94
Thus, the probability that a plan arrives on time given that it departed on time is 0.94.
b) Probability that a plan arrives on time given that it departed on time:
The probability that a plan arrives on time given that it departed on time is calculated as follows:
P (D/A)= probability that the plan arrives on time given that it departed on time
P (D/A)= (P (D ∩ A))/(P (A))
= (0.78)/(0.82)
P (D/A)=0.95
Thus, the probability that a plan arrives on time given that it departed on time is 0.95.