The probability that a regulary seheduted flightdeparts on time is 0.8

jippie771h

jippie771h

Answered question

2021-11-16

The probability that a regulary seheduted flightdeparts on time is 0.83 ,
the probability that it arrives on time is 0.92 and the probability that it departs
and arrives on time is 0.78 . Find the probability thata plane
(1) arrives on time given thatit departed on time .
(2) departed on time given that it has arrived on time .

Answer & Explanation

Edward Belanger

Edward Belanger

Beginner2021-11-17Added 11 answers

Step 1
Probability of an event is ratio of total number of favourable outcomes for the event to total number of possible outcomes of the experiment. If there are two event A and B, the probability of event A when event B has already been occurred, is called conditional probability.
The formula of conditional probability is P(AB)=P(AB)P(B) the value P(AB) represents the probability when both the events A and B occurs together.
Step 2
Lets A denotes the event that flight arrives on time and 8 represents the event that the flight departures on time, So the given probabilities are P(A)=0.92, P(D)=0.83 and P(AD)=0.7 and P(AD)=0.78.
For the first part, apply the conditional probability formula to find the value of P(AD) and substitute the values.
P(A|D)P(AD)P(D)
=0.780.83
0.94
So the probability that the arrival is on time when the departure was on time will be approximately 0.94.
Step 3
For the next part, apply the conditional probability formula to find the value of P(DA) and substitute the values.  P(D|A)P(AD)P(A)
=0.780.92
0.85
So the probability that the departure was on time when the arrival was on time will be approximately 0.85.

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