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The probability that a 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, computed to the nearest two decimal points.

Respuesta :

Solution: Let P(A) denotes the probability that the plane arrives on time and let P(D) denotes the probability that the plane departs on time. Therefore, we have:

[tex]P(A) = 0.82, P(D)=0.83, P(A \cap D)=0.78[/tex]

Now the probability that a plane arrives on time given that it departs on time is:

[tex]P(A|D) = \frac{P(A \cap D)}{P(D)}[/tex]

                  [tex]=\frac{0.78}{0.83} =0.94[/tex]

Therefore, the probability that a plane arrives on time given that it departs on time = 0.94

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