Question

The probability that a train leaves on time is 0.90. The probability that this train both leaves on time and arrives on time is 0.75. If the train leaves on time, then what is the probability that is also arrives on time?.

Answer 1

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

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:

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:

We know

that is also means :

Thus we get:

Thus

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