In the last round of a chess tournament the final match is between Alice and Diego. The winner is the first player to win three games [sometimes called "best of 5"]. Assume that they are equally matched, so that each player has an equal probability of winning each game. What is the probability that the match will be finished after the first 3 games are played?

An optical inspection system is used to distinguish among different part types. the probability of a correct classification of any part is 0.92. suppose that three parts are inspected and that the classifications are independent. let the random variable x denote the number of parts that are correctly classified. determine the probability mass function of x. round your answers to four decimal places (e.g. 98.7654). x f(x) 0 1 2 3