Problem 199SE

When a bus service reduces fares, a particular trip from New York City to Albany, New York, is very popular. A small bus can carry four passengers. The time between calls for tickets is exponentially distributed with a mean of 30 minutes. Assume that each caller orders one ticket. What is the probability that the bus is filled in less than three hours from the time of the fare reduction?

Solution:

Step 1 of 2:

It is given that a small bus can carry 4 passengers.The bus service reduces the fares of a particular journey.

The time between calls for ticket booking is Exponentially distributed with a mean of 30 minutes,

Also, it is assumed that each caller books one ticket.

Using this we need to find the probability that the bus is filled in less than three hours.