5. Analyzing a binomial experiment using a tree diagram Data from the U.S. Bureau of Labor Statistics show a steady decline in the average workweek of U.S. production workers from 38.5 hours in 1964 to 33.9 hours in 2006. But employees are spending time working when they are at home and behind the wheel. In a poll conducted for Staples, 18% of small business managers in the United States reported that they read e-mail messages in the bathroom. [Source: Lisa Belkin, "Time Wasted? Perhaps it's Well Spent," The New York Times, May 31, 2007.) Consider the experiment of randomly selecting four small-business managers and learning whether they read e-mail messages in the bathroom. Let R = reads e-mail in the bathroom, and N = does not read e-mail in the bathroom The experiment satisfies the properties of a binomial experiment. The following tree diagram will help you visualize the sample space for this experiment. First Trial Second Trial Third Trial Fourth Trial (RR,RR) R 18 N R 18 (R. R. RN N (R, R, N, R) 82 R 18 N (R, R, N, N) (R, N, RR) 1 R .18 N N R / .18 (R. N, R, ND .18 N R .18 N (R, N, NLR) (R, N, N, N) (N, R. RR) R 18 N R (N, R, RN) R. (N, R, N, R) 18 R 18 N 3/ (N, R, N, N) (N, N, RR) N R 18 N R .82 (N, N, R, N) N 18 N (N, N, N, R) (N, N, N, N) .18 (R, N, N, R) R .18 N .82 (R, N, N, N) (N, R, R, R) R .18 N R .18 (N, R, R, N) .82 N N R (N, R, N, R) .82 .18 .82 R .18 N .82 (N, R, N, N) R (N, N, R, R) N .18 R .18 .82 .82 (N, N, R, N) R N .82 (N, N, N, R) .82 (N, N, N, N) First, define a success. In this case, define the selection of a manager who reads e-mail in the bathroom as a success. Of the possible experimental outcomes, outcomes result in exactly three successes. 12 16 All of the sampl with three successes have the same probability of occurrence. What is this probability? 10 2 8 0.0048 0.0058 0.0218 0.0992 The probability that exactly three managers read e-mail messages in the bathroom is