Hello, thesocialnetwork!

Here's part (a) . . .

Herman and Amos are usually late for school.

Herman travels to school either by train, bus or taxi with the probability of 2/5, 2/5 and 1/5 respectively.

His classmate Amos will only travel by bus or taxi with probability of 3/4 for travelling by bus.

Herman has the probability 1/4, 1/2 and 1/4 of being late when he travels by the train, bus or taxi respectively.

Amos has the probability of 3/5 and 1/5 of being late when he travels by bus or taxi respectively.

Find the probability that: (a) Either of them is late.

We want: . .[1]

Herman

.

Amos

. .

Hence: .

Substitute into [1]:

. . . .