# 18, 31, 32, 33, 34, 36, 38Sorry for all the questions. I just hate paying 3$ per question. Thank you!
18. A game involves tossing two coins and receiving 50e if they 37. In old gangster movies on TV, you often hear of "number are both heads. What is a fair price to pay for the privilege of runners" or the "numbers racket." This numbers game, which playing? is still played today, involves betting $1 on the last three digs. 19. Krinkles potato chips is having a "Lucky Seven Sweepstakes." of the number of stocks sold on a particular day in the future The one grand prize is $70,000; 7 second prizes each pay reported in The Wall Street Journal. If the payoff is $500, whit is the expectation for this numbers game? $7,000; 77 third prizes each pay $700; and 777 fourth prizes each pay $70. What is the expectation of this contest, if there 38. In a TV game show, four prizes are hidden on a game board are 10 million entries? that contains 20 spaces. One prize is worth $10,000, two 20. A punch-out card contains 100 spaces. One space pays $100, Prizes are worth $5,000, and the other prize is worth $1,00 five spaces pay $10, and the others pay nothing. How much The remaining spaces contain no prizes. The game show should you pay to punch out one space? host offers a sure prize of $1,000 not to play this game. Should the contestant choose the sure prize or play the game? Level 2 39. Suppose it costs $2,400 to advertise and list a $350,000 What is the expectation for the $1 bets in Problems 21-30 on a house for sale. The listing agent will earn 5% of the selling U.S. roulette wheel? See Figure 13.8 on page 616. price if the listing agent sells the property, but only 2.5% 21. Black 22. Odd if the house is sold by another agent. If the house is unsold 23. Single-number bet 24. Double-number bet after 4 months, the listing (and the cost of advertising) will be lost. Suppose that the probabilities for selling the house 25. Three-number bet 26. Four-number bet are as follows: 27. Five-number bet 28. Six-number bet 29. Twelve-number bet 30. Column bet Event Probability Consider the spinners in Problems 31-34. Determine which represent Sells the house alone 0.40 fair games. Assume that the cost to spin the wheel once is $5.00 and Sells through another agent 0.30 that you will receive the amount shown on the spinner after it stops. Does not sell in 4 months 0.30 31. 32. What is the expected profit from listing on this house? $8.00 $5.0 40. A realtor who takes the listing on a house to be sold knows that she will spend $800 trying to sell the house. If she sells $0 $10.00 it herself, she will earn 6% of the selling price. If another $2.00 realtor sells a house from her list, the first realtor will earn only 3% of the price. If the house remains unsold after 6 33. 34. months, she will lose the listing. Suppose that the probabili- ties are as follows: 0O'DL$ $8.00 $8.00 Event Probability $2.00 $2.00 Sells the house alone 0.50 $4.00 $5.00 Sells through another realtor 0.30 Does not sell in 6 months 0.20 35. Assume that a dart is randomly thrown at the dartboard shown here and strikes the board every time. The payoffs are listed What is the expected profit from listing a $185,000 house? on the board. How much should you be willing to pay for the 41. An oil-drilling company knows that it costs $25,000 to opportunity to play this game? sink a test well. If oil is hit, the income for the drilling company will be $425,000. If only natural gas is hit, the $6.00 income will be $125,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the $1.00 $8.00 probability of hitting gas is 1/20, what is the expectation $10.00 for the drilling company? Should the company sink the $4.00 test well? 36. Assume that a dart is randomly thrown at the dartboard shown 42. In Problem 41, suppose that the income for hitting oil is here and strikes the board every time. The payoffs are listed changed to $825,000 and the income for gas to $225,000. Now on the board. How much should you be willing to pay for the what is the expectation for the drilling company? Should the opportunity to play this game? company sink the test well? $16 43. Consider the following game in which a player rolls a single die. If a prime (2, 3, or 5) is rolled, the player wins $2. If a -$5 $2 $1 square (1 or 4) is rolled, the player wins $1. However, if the $8 player rolls a perfect number (6), it costs the player $11. Is this $4 a good deal for the player or not
