Probability (9E) - Ross. Prob 4.72, 4.79: Random Variables/Probabilities

A First Course in Probability (Ninth Edition) - Sheldon Ross Chapter 4: Random Variables 4.1: Random Variables 4.2: Discrete Random Variables 4.3: Expected Value 4.4: Expectation of a Function of a Random Variable 4.5: Variance 4.6: The Bernoulli and Binomial Random Variables 4.7: The Poisson Random Variable 4.8: Other Discrete Probability Distributions 4.9: Expected Value of Sums of Random Variables 4.10: Properties of the Cumulative Distribution Function Prob 4.72: Two athletic teams play a series of games; the first team to win 4 games is declared the overall winners. Suppose that one of the teams is stronger than the other and wins each game with probability 0.6, independently of the outcomes of the other games. Find the probability, for i = 4, 5, 6, 7, that the stronger team wins the series in exactly games. Compare the probability that the stronger team wins with the probability that it would win a 2-out-of-3 series. Prob 4.79: Suppose that a batch of 100 items contains 6 that are defective and 94 that are not defective. If X is the number of defective items in a randomly drawn sample of 10 items from the batch, find P(X = 0) and (b) P(X greater than 2).