There are two cashiers iii a bank Jack Jill and Kathy enter

There are two cashiers iii a bank. Jack, Jill and Kathy enter the bank simultaneously. Jack and Jill go directly to the cashiers and Kathy waits until either Jack or Jill leaves before she begins service. What is the probability that Jack is still in the bank after the other two have left when: (a) the service time for each cashier is exactly 5 minutes (b) the service time for each cashier is exponential with mean of 5 minutes

Solution

Prob (Jack waits after Kathy and Jill left)

= Prob (Jack waits when Jill left and Kathy has gone to the II cashier)

= P(I cashier time t > 5 minutes and II cashier time <t/2 minutes)

=P(I cashier takes more than 10 minutes)

= P( time >10) for a POisson with average time 5

= 0.03182