Question

The probability that a train leaves on time is 0.7. The probability that the train arrives on time and leaves on time is 0.56. What is the probability that the train arrives on time, given that it leaves on time?

Answer 1

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Answer 2

Solution:

We are given that:

The probability that a train leaves on time is 0.90.

Let A = train leaves on time

then we have P(A 1) = 0.90

The probability that this train both leaves on time and arrives on time is 0.75.

Let B = train arrives on time

Thus we have:

P(A n B) = 0.75

If the train leaves on time, then what is the probability that is also arrives on time?.

That is we have to find:

P( Train arrives on time given that the train leaves on time) = .........?

That is we have to find:

P( B | A) =.........?

Using conditional probability formula:

PlBA) = PPAA ( )

We know P(A n B) = 0.75

that is also means : P(B n A) = 0.75

Thus we get:

PlBA) = PPAA ( )

0.75 P(BIA) = 0.00 2

P(BA)0.833333

P(BIA) = 0.8333

Thus

P( Train arrives on time given that the train leaves on time) = 0.8333