The phone lines to an airline reservation system are occupie

The phone lines to an airline reservation system are occupied 50% of the time. Assume that the events that the lines are occupied on successive calls are independent. Assume that 10 calls are placed to the airline. What is the probability that for exactly three calls the lines are occupied? What is the probability that for at least one call the lines are not occupied? What is the expected number of calls in which the lines are all occupied?

Solution

Given X~Binomial(n=10, p=0.4) P(X=x)=xC10*(0.4^x)*(0.6^(10-x)) a.P(X=3)=3C10*(0.4^3)*(0.6^(10-3))=0.2149908 b. P(X>=1)=1-P(X=0)=1-0.6^10=0.9939534 c. mean=n*p=10*0.4=4