Question

John needs to catch a train. The train arrives randomly some time between 2:00 and 3:00, waits for 20 minutes, and then leaves. If John also arrives randomly between 2:00 and 3:00, what is the probability that the train will be there when John arrives?

Answer 1

Answer:

$\frac{1}{16}$

Step-by-step explanation:

If train arrives between 2:00 to 3:00 (60min) and waits for 20 min and leaves, probability of finding train in that 60 min is $\frac{20}{60}=\frac{1}{3}$.

Probability of finding John is $\frac{1}{60}$ can arrive any minute.

now the probability of finding both john and train is $\frac{1}{60}$*$\frac{20}{60}$=$\frac{1}{16}$.

This is compound Probablity Problem.