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: . .
Substitute into :
. . . .