Summary: ISyE 6650 Exam # 1
Please be neat and show all your work so that I can give you partial credit.
(40) 1. Two players A and B take turns to play on a gaming machine. All plays
are independent. A plays first. On his turn, A can score a success against the
machine with probability a; B with probability b. The first to score a success
wins. (If A scores a success in the first game, B never plays).
(15) (a) What is the probability that A wins the game?
(15) (b) What is the expected number of games that A plays?
(10) (c) What is the expected number of games that B plays?
(30) 2. A machine produces two items per day. The probability that an item is
non-defective is p. Defective items are thrown away instantly. The demand is