688 CHAPTER 11 Probability 29. The checks in the envelopes are for $0, $2, $5, and $20, respectively. −$8.25 30. The checks in the envelopes are for $2, $2, $100, and $400, respectively. $111.00 31. Job Openings There is a 20% chance that next year the total number of employees in the Menards stores in Milwaukee will increase by 300. There is a 70% chance that the increase will be 400 employees, and a 10% chance the total number of employees will decrease by 500. Determine the expected gain or loss in the number of employees for next year. Gain of 290 employees 32. Life Insurance According to Bristol Mutual Life Insurance’s mortality table, the probability that a 20-yearold woman will survive 1 year is 0.994 and the probability that she will die within 1 year is 0.006. If a 20-year-old woman buys a $10,000 1-year policy for $100, what is Bristol Mutual’s expected gain or loss? $40.00 gain 33. Fire Auxiliary When Christina attends a fire auxiliary event, she is given one free ticket for the $1000 door prize. A total of 500 tickets will be given out. Determine Christina’s expectation of winning the door prize. $2 34. Fishing Festival At the annual Fishing Festival, all attendees’ names are entered into a drawing for a grand prize of $100. Tim is among the 250 attendees. Determine Tim’s expectation of winning the grand prize. $0.40 35. 4H Club Fundraiser The Hazel Green Clever Clovers 4H club is selling raffle tickets to raise money for an upcoming trip to an amusement park. Tickets sell for $10 each and there are 200 tickets sold. The grand prize is $500. If Charlotte buys one ticket, determine her expectation of winning the grand prize. $7.50 − 36. Boys and Girls Clubs The Boys and Girls Clubs of Darlington County are selling raffle tickets to raise money for a new youth center. Tickets sell for $100 each and 500 tickets are sold. The grand prize is $1000. If Lamar purchases one ticket, determine his expectation of winning the grand prize. $98 − 37. Veterans Fundraiser At a fundraiser for the local veterans association, 500 raffle tickets are sold for $5 each. One grand prize of $1000 and two consolation prizes of $250 will be awarded. Assume the probability that any given ticket selected for the grand prize is 1 500 and the probability that any given ticket selected for a consolation prize is . 2 500 Determine number. Determine the person’s expectation if the person plays the game. 21. 2$15 2$2 $5 −$1.75 22. $20 $2 –$10 $0.50 Selecting an Envelope In Exercises 23–26, a person randomly selects one of the following six envelopes. Each envelope contains a check that the person gets to keep. Determine the person’s expectation if the checks in the envelopes are as indicated in the exercises. 1 2 4 3 5 6 23. Three envelopes contain a $500 check, and three envelopes contain a $1000 check. $750 24. Four envelopes contain a $1000 check, and two envelopes contain a $5000 check. $2333.33 25. The six envelopes contain checks for $100, $200, $300, $400, $500, and $1000, respectively. $416.67 26. Two envelopes contain a check for $600, two envelopes contain a check for $2000, and two envelopes contain a check for $5000. $2533.33 Selecting an Envelope In Exercises 27–30, a person randomly selects one of the following four envelopes. Each envelope contains a check that the person gets to keep. However, before the person can select an envelope, they must pay $15 to play. Determine the person’s expectation if the checks in the envelopes are as indicated in the exercises. 1 3 2 4 27. Two envelopes contain a $10 check, and two envelopes contain a $25 check. $2.50 28. Three envelopes contain a $20 check, and one envelope contains a $0 check. $0 Rocksweeper/Shutterstock
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