Question

Buses to A leave a bus station on the hour and at every 10 minute intervals thereafter. Buses to B leave from the same bus station on the hour and at 15 minute intervals thereafter. A woman arrives at the bus station and since her destination is both on the A and B routes, she takes the first bus that leaves. Find the probability that her bus is going to A if
(i) at the hour the bus to A always leaves before the bus B
ii) at the hour the bus to B always leaves before the bus to A
iii) at the hour the chances of A bus and B bus are equally likely
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Answer 1

Answer:

Mi latif how are you friend

Answer 2

Given:

Time interval

For Bus A:   0, 10, 20, 30, 40, 50  

For Bus B:   0, 15, 30, 45

To Find:

The probability that her bus is going to A if

(i) at the hour the bus to A always leaves before the bus B

ii) at the hour the bus to B always leaves before the bus to A

iii) at the hour the chances of A bus and B bus are equally likely

Solution:

i) The probability that her bus is going to A if at the hour the bus to A always leaves before the bus B,

Since bus A goes 6 times at intervals in an hour

                          P = 6/8

                              = 3/4

ii)The probability that her bus is going to A if at the hour the bus to B always leaves before the bus to A

Since bus B goes 4 times at intervals in an hour

                           P = 4/8

                               = 1/2

iii)The probability that her bus is going to A if at the hour the chances of A bus and B bus are equally likely

In this case, there are 10 possibles

                           P = 6/10

                               = 3/5

Hence, found.

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