Example Probability Problems Taken from http://myphliputil.pearsoncmg.com/student/bp_render_qam_8/internetHW_ch2.doc
Problem 2-50 • This year Jan Rich, who is ranked number one in women's singles in tennis, and Marie Wacker, who is ranked number three, will play 4 times. If Marie can beat Jan 3 times, she will be ranked number one. The two players have played 20 times before, and Jan has won 15 games. It is expected that this pattern will continue in the future. What is the probability that Marie will be ranked number one after this year? What is the probability that Marie will win all 4 games this year against Jan?
Problem 2-51 • Over the last two months, the Wilmington Phantoms have been encountering trouble with one of their star basketball players. During the last 30 games, he has fouled out 15 times. The owner of the basketball team has stated that if this player fouls out 2 more times in their next 5 games, the player will be fined $200. What is the probability that the player will be fined? What is the probability that the player will foul out of all 5 games? What is the probability that the player will not foul out of any of the next 5 games?
Problem 2-52 • Wisconsin Cheese Processor, Inc., produces equipment that processes cheese products. Ken Newgren is particularly concerned about a new cheese processor that has been producing defective cheese crocks. The piece of equipment produces 5 cheese crocks during every cycle of the equipment. The probability that any one of the cheese crocks is defective is 0.2. Ken would like to determine the probability distribution of defective cheese crocks from this new piece of equipment. The number of defectives can be 0, 1, 2, 3, 4, or 5. Find the probability of each of these. What is the expected value and variance of this distribution?
2-53 • Natway, a national distribution company of home vacuum cleaners, recommends that its salespersons make only two calls per day, one in the morning and one in the afternoon. Twenty-five percent of the time a sales call will result in a sale, and the profit from each sale is $125. Develop the probability distribution for sales during a five-day week. What is the mean and variance of this distribution? What is the expected weekly profit for a salesperson?