2 The probability is p that Marty hits target M when he fires at it. The probability is q that Alvie hits target A when he fires at it. Marty and Alvie fire one shot each at their targets. If both of them hit their targets, they stop; otherwise, they will continue.

(a) What is the probability that they stop after each has fired r times?

(b) What is the expected value of the number of the times that each of them has fired before stopping?.