In the game show The Price Is Right, two players get to spin a wheel with the values 05, 10, 15, . . . . , 95, 100 on it. In the game, Player 1 spins the wheel one time and gets to decide whether he/she would like to spin a second time in the hope that the sum of the two values gets closer to, but does not exceed 100. Player 2 then spins the wheel; if the value shown is less than the score earned by Player 1, the player must spin again. If the second spin results in a sum less than that earned by Player 1 or greater than 100, Player 2 loses; if the second spin results in a sum greater than that earned by Player 1, but less than or equal to 100, Player 2 wins. If the two spins result in the same value as Player 1, the player's tie. Suppose Player 1 ends up with 80 points. The data set 5_6_3 located at www.pearsonhighered.com/sullivanstats represents simulated results. Use these simulated results to approximate the following probabilities.
(a) Explain how to do a simulation to determine the probability that Player 2 will beat Player 1.
(b) The column “Outcome_Spin1” represents the results of the first spin by Player 2. What is the probability Player 2 wins on the first spin?
(c) What is the probability Player 2 ties on the first spin?
(d) The results in the column “Strategy1” represents simulated results assuming the player does not accept the tie if Spin 1 results in 80. In the case of a tie after Spin 1, there is a second spin. In the case of a tie after Spin 2, there is a one-spin playoff. The results of any playoff are in the columns “Player1_Spin3” and “Player2_Spin3”. Explain the sequence of events that led Player2 to win the game in Row 1. Explain the sequence of events that led Player 2 to lose the game i Row 68.
(e) What is the probability of Player 2 winning the game following Strategy 1?
(f) The results in the column “Strategy2” represent simulated results assuming the player accepts the tie if Spin 1 results in 80. In the case of a tie after Spin 1, there is a one-spin playoff. The results of any playoff are in the columns “Player1_Spin3” and “Player2_Spin3”. Explain the sequence of events that led Player 2 to lose the game in Row 72.
(g) What is the probability of Player 2 winning the game following Strategy 2?
(h) Recommend a strategy for Player 2 to follow based on the results of parts (e) and (g).