(d) As the mechanic has decided to check two machines, therefore, if he identifies either both defective machines or both non-defective then the probability that he is able to catch the last bus is sum of the two. Following table gives the possible outcome and their corresponding probabilities.
Outcome
Probability
1
def def
(
1
2
)(
1
3
)=
1
6
2
def non def
(
1
2
)(
2
3
)=
1
3
3
non def def
(
1
2
)(
2
3
)=
1
3
4
non - def non - def
(
1
2
)(
1
3
)=
1
6
In the first and last cases, the mechanic would have identified the defective machines in time to catch the bus. ∴ Probability that he is able to catch the last bus is