When he arrives, he is late What is the probability
that he comes by train Solution Let E be the event that the doctor visits the patient late and let T1, T2, T3, T4
be the events  that the doctor comes by train, bus, scooter, and other means of transport
respectively Then
P(T1) =
2
3
4
3
1
1
2
, P(T )
,P(T )
and P(T )
10
5
10
5
=
=
=
(given)
P(E|T1) = Probability that the doctor arriving late comes by train = 1
4
Similarly, P(E|T2) = 1
3 , P(E|T3) = 1
12  and P(E|T4) = 0, since he is not late if  he
comes by other means of transport