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

Answer: The required probability is 0.8.

Step-by-step explanation: Let, 'E' denotes the event that a train leaves on time and 'F' denotes the event that the train arrives on time.

Then, according to the given information,

`P(E)=0.7.`

The event that the train arrives on time and leaves on time will be
`F\cap E.`

So,

`P(F\cap E)=0.56.`

We are to find the probability that the train arrives on time, given that it leaves on time, ie., P(F/E).

We have

`P(F/E)=(P(F\cap E))/(P(E))=(0.56)/(0.7)=(56)/(70)=0.8.`

Thus, the required probability is 0.8.