Question

P.8 A post office is run by two clerks. Mr. Smith enters the office and finds the two clerks busy serving Mr. Jones and Mr. Brown. The amount of time a clerk spends with a customer is exponentially distributed with mean 20 minutes I (a) What is the probability that, out of the three customers Mr. Smith is the last to leave the post office? (b) What is the probability that Mr. Smith waits for 30 minutes before being served?

Answer 1

a) Mr. smith to leave the postoffice he must be served, Mr. Smith to be served either of the clerk should become free which mean Mr. Jones or Mr. Brown should leave the post office. Lets assume if Mr.Brown left the post office now there are only two coustmers who are smith and Jones. It is given serving time follows exponential distribution, since this distribution is memoryless distribution now it can consider that Jone's is serving is again started along with smith. Since now there are only two persons the probability that Mr. Smith leaves the postoffice last will be 0.5.

b) Given mean = 20 minutes

$\lambda$ = 1/20

P(X=30) = = 0.223.

-30 30/20