The probability that a regularly scheduled flight departs on time is P

deliredejoker7m

deliredejoker7m

Answered question

2021-11-14

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(DA)=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

Answer & Explanation

Alfonso Miller

Alfonso Miller

Beginner2021-11-15Added 20 answers

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(DA)=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(AD)= probability that the plan arrives on time given that it departed on time
P(AD)=P(AD)P(D)
=0.780.83
P(AD)=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(DA)= probability that the plan arrives on time given that it departed on time
P(DA)=P(DA)P(A)
=0.780.82
P(DA)=0.95
Thus, the probability that a plan arrives on time given that it departed on time is 0.95.
Vasquez

Vasquez

Expert2023-06-11Added 669 answers

Answer:
a. P(A|D)0.9398
b. P(D|A)0.9512
Explanation:
a. To find the probability that a plane arrives on time given that it departed on time, we need to find P(A|D). This represents the probability of the plane arriving on time (A) given that it departed on time (D).
According to the formula for conditional probability, we have:
P(A|D)=P(AD)P(D)
Here, P(A ∩ D) represents the probability that the plane both departs and arrives on time, which is given as 0.78. P(D) represents the probability that the plane departs on time, which is given as 0.83.
Substituting the values into the formula, we get:
P(A|D)=0.780.830.9398
Therefore, the probability that a plane arrives on time given that it departed on time is approximately 0.9398.
b. Similarly, to find the probability that a plane departed on time given that it has arrived on time, we need to find P(D|A). This represents the probability of the plane departing on time (D) given that it arrived on time (A).
Using the formula for conditional probability, we have:
P(D|A)=P(DA)P(A)
Here, P(D ∩ A) represents the probability that the plane both departs and arrives on time, which is given as 0.78. P(A) represents the probability that the plane arrives on time, which is given as 0.82.
Substituting the values into the formula, we get:
P(D|A)=0.780.820.9512
Therefore, the probability that a plane departed on time given that it has arrived on time is approximately 0.9512.
nick1337

nick1337

Expert2023-06-11Added 777 answers

a. 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)
Substituting the given values:
P(A|D)=0.780.83=0.939
Therefore, the probability that a plane arrives on time given that it departed on time is 0.939.
b. To find the probability that a plane departed on time given that it has arrived on time, we can use the conditional probability formula:
P(D|A)=P(DA)P(A)
Substituting the given values:
P(D|A)=0.780.82=0.951
Therefore, the probability that a plane departed on time given that it has arrived on time is 0.951.

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