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What is the probability that player 1 will win?
Q. Two players compete in a game of chance involving a pair of fair dice. Player 1 rolls first and wins if she rolls a 7. Player 2 wins if he rolls a 7 or a 12. Play alternates until a player wins. What is the probability that player 1 will win?
Asked by TNT - Thu May 28 15:34:25 2009 - - 4 Answers - 2 Comments
A. Ways to roll a 7: 1+6 6+1 2+5 5+2 3+4 4+3 so 6. 6/36 = 1/6% of a win when rolling. Player 2 has a 7/36 chance of winning, which is a little over 1/6%. On the first roll, player 1 has a chance of 1/6. The probability of winning will change, because his second roll depends if player 2 loses now. Chance of player 2 losing is 36-7/36 = 29/36. So we mulitply 1/6 * 29/36 for the probability of player 2 losing AND player 1 winning on the second roll. If you want to know the probability that player 1 will win a roll, it's 1/6. If you want the probability that player 1 will win the game, it will fluxuate because the events depend on the earlier rolls all losing.
Answered by Sekida - Thu May 28 15:43:20 2009
Q. Two players compete in a game of chance involving a pair of fair dice. Player 1 rolls first and wins if she rolls a 7. Player 2 wins if he rolls a 7 or a 12. Play alternates until a player wins. What is the probability that player 1 will win?
Asked by TNT - Thu May 28 15:34:25 2009 - - 4 Answers - 2 Comments
A. Ways to roll a 7: 1+6 6+1 2+5 5+2 3+4 4+3 so 6. 6/36 = 1/6% of a win when rolling. Player 2 has a 7/36 chance of winning, which is a little over 1/6%. On the first roll, player 1 has a chance of 1/6. The probability of winning will change, because his second roll depends if player 2 loses now. Chance of player 2 losing is 36-7/36 = 29/36. So we mulitply 1/6 * 29/36 for the probability of player 2 losing AND player 1 winning on the second roll. If you want to know the probability that player 1 will win a roll, it's 1/6. If you want the probability that player 1 will win the game, it will fluxuate because the events depend on the earlier rolls all losing.
Answered by Sekida - Thu May 28 15:43:20 2009
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