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Math
Probability
Consider the following game. A player throws a fair die repeatedly until he rolls a 2, 3, 4, 5, or 6. In other words, the player continues to throw the die as long as he rolls 1s. When he rolls a "non-1," he stops. (a) What is the probability that the player tosses the die exactly five times? (Round your answer to four decimal places.) (b) What is the expected number of rolls needed to obtain the first non-1? (c) If he rolls a non-1 on the first throw, the player is paid $1. Otherwise, the payoff is doubled for each 1 that the player rolls before rolling a non-1. Thus, the player is paid $2 if he rolls a 1 followed by a non-1; $4 if he rolls two 1s followed by a non-1; $8 if he rolls three 1s followed by a non-1; etc. In general, if we let y be the number of throws needed to obtain the first non-1, then the player rolls (Y-1) 1s before rolling his first non-1, and he is paid 2Y - 1 dollars. What is the expected amount in dollars paid to the player? $

Consider the following game. A player throws a fair die repeatedly until he rolls a 2, 3, 4, 5, or 6. In other words, the player continues to throw the die as long as he rolls 1s. When he rolls a "non-1," he stops. (a) What is the probability that the player tosses the die exactly five times? (Round your answer to four decimal places.) (b) What is the expected number of rolls needed to obtain the first non-1? (c) If he rolls a non-1 on the first throw, the player is paid $1. Otherwise, the payoff is doubled for each 1 that the player rolls before rolling a non-1. Thus, the player is paid $2 if he rolls a 1 followed by a non-1; $4 if he rolls two 1s followed by a non-1; $8 if he rolls three 1s followed by a non-1; etc. In general, if we let y be the number of throws needed to obtain the first non-1, then the player rolls (Y-1) 1s before rolling his first non-1, and he is paid 2Y - 1 dollars. What is the expected amount in dollars paid to the player? $

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 105CR
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22 Consider the following game. A player throws a fair die repeatedly until he rolls a 2, 3, 4, 5, or 6. In other words, the player continues to throw the die as long as he rolls 1s. When he rolls a "non-1," he stops. (a) What is the probability that the player tosses the die exactly five times? (Round your answer to four decimal places.) (b) What is the expected number of rolls needed to obtain the first non-1? (c) If he rolls a non-1 on the first throw, the player is paid $1. Otherwise, the payoff is doubled for each 1 that the player rolls before rolling a non-1. Thus, the player is paid $2 if he rolls a 1 followed by a non-1; $4 if he rolls two 1s followed by a non-1; $8 if he rolls three is followed by a non-1; etc. In general, if we let y be the number of throws needed to obtain the first non-1, then the player rolls (Y− 1) 1s before rolling his first non-1, and he is paid 2Y - 1 dollars. What is the expected amount in dollars paid to the player? $
Transcribed Image Text:22 Consider the following game. A player throws a fair die repeatedly until he rolls a 2, 3, 4, 5, or 6. In other words, the player continues to throw the die as long as he rolls 1s. When he rolls a "non-1," he stops. (a) What is the probability that the player tosses the die exactly five times? (Round your answer to four decimal places.) (b) What is the expected number of rolls needed to obtain the first non-1? (c) If he rolls a non-1 on the first throw, the player is paid $1. Otherwise, the payoff is doubled for each 1 that the player rolls before rolling a non-1. Thus, the player is paid $2 if he rolls a 1 followed by a non-1; $4 if he rolls two 1s followed by a non-1; $8 if he rolls three is followed by a non-1; etc. In general, if we let y be the number of throws needed to obtain the first non-1, then the player rolls (Y− 1) 1s before rolling his first non-1, and he is paid 2Y - 1 dollars. What is the expected amount in dollars paid to the player? $
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