Question

The probability that a train leaves on time is 0.4. The probability that the train arrives on time and leaves on time is 0.28. What is the probability that the train arrives on time, given that it leaves on time?
0.4
0.12
0.28
0.7

Answer 1

You need to use the conditional probability formula:
P(A|B) = P(A∩B) / P(B)
Key:
P(A|B): Probability of A given B
P(A∩B): Probability of A and B

If we say A is the event that the train arrives on time and B is the event that the train leaves on time, then according to the information:
P(B) = 0.4
P(A∩B) = 0.28
Just insert into the formula:
P(A|B) = 0.28 / 0.4 = 0.7
(or 70% as a percentage).