Question

A train and a bus arrive at the station at random between 9 A.M. and 10 A.M. The train stops for 10 minutes and the bus for x minutes. Find x so that the probability that the bus and the train will meet equals 0.5. Explain step by step solution with diagram.

Answer 1

There is total 60 minute time in which the train at the station for 10 minutes.

i.e. p(the train at the station) = 10/60 = 1/6

similarly

p(the bus at the station) = x/60 (since the bus stop at the station for x minutes)

we have to find the probability that both are at the station and which needs to be 0.5.

p(both the train and the bus at the station)=p(the train at the station)*p(the bus at the station)

0.5 = (1/6)*(x/6)

0.5=x/36

i.e. x = 0.5*36 = 18

That means, the bus stop at the station for 18 minutes so the probability that the bus and the train will meet equal 0.5.