Amy and Bruce are playing a game where a player wins as soon as s/he has two points more than his/her opponent. Both players start at par, and points are earned one at a time. If Amy has a 5/6 chance of winning each point, what is the probability that she will win the game? Give your answer as a fraction reduced to lowest terms. ^can somebody pm me or post the answer to that please? I can throw in a free neopets 4 month+ shell if you do. Show your work aswell
Do they specify how many rounds a game there are? Ideally you'd use a probability tree diagram like this: https://nrich.maths.org/discus/messages/67613/67821.jpg Not knowing how many rounds there are though...?
I'm a little rusty but let me give this a try... b(2; 2, 5/6) = 2C2 * (5/6)2 * (1 - 5/6)2-2 = ((2 * (2-1)) / 2!) * 25/36 * (1/6)0 = ((2 * 1) / (2 *1)) * 25/36 * 1 = (2 / 2) * 25/36 = 25/36 Can someone double check for me?
Yep, the answer is 25/36. Amy 5/6 chance Ben 1/6 chance So (5/6 * 5/6) because you are looking at the chance Amy will win the game. That is 25/36. (Of course, you have to count in the chance that it still draw after 2 Rounds [1/6 * 5/6] + [5/6 * 1/6] = 5/18. But if it's draw, the game is back to where it started and you go play another 2 rounds. Amy: 25/36 Draw: 10/36 Ben: 1/36