The showcase showdown. On the popular television game show The Price Is Right, contestants can play "The Showcase Showdown." The game involves a large wheel with 20 nickel values, 5, 10, 15, 20, . . . , 95, 100, marked on it. Contestants spin the wheel once or twice, with the objective of obtaining the highest total score without going over a dollar (100). [According to the American Statistician (August 1995), the optimal strategy for the first spinner in a three-player game is to spin a second time only if the value of the initial spin is 65 or less.] Let x represent the total score for a single contestant playing “The Showcase Showdown.” Assume a “fair” wheel (i.e., a wheel with equally likely outcomes). If the total of the player's spins exceeds 100, the total score is set to 0.
- a. If the player is permitted only one spin of the wheel, find the
probability distribution for x. - b. Refer to part a. Find E (x) and interpret this value.
- c. Refer to part a. Give a
range of values within which x is likely to fall. - d. Suppose the player will spin the wheel twice, no matter what the outcome of the first spin. Find the probability distribution for x.
- e. What assumption did you make to obtain the probability distribution, part d? Is it a reasonable assumption?
- f. Find f. L and u for the probability distribution, part d. and interpret the results.
- g. Refer to part d. What is the probability that in two spins the player's total score exceeds a dollar (i.e., is set to 0)?
- h. Suppose the player obtains a 20 on the first spin and decides to spin again. Find the probability distribution for x.
- i. Refer to part h. What is the probability that the player's total score exceeds a dollar?
- j. Given the player obtains a 65 on the first spin and decides to spin again, find the probability that the player's total score exceeds a dollar.
- k. Repeat part j for different first-spin outcomes. Use this information to suggest a strategy for the one-player game.
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