SOLUTION: A and B play a game in which B's probability of winning is 2/3 if they play five games what is probability A will win atleast one game

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Question 858001: A and B play a game in which B's probability of winning is 2/3 if they play five games what is probability A will win atleast one game
Answer by ben720(159) About Me  (Show Source):
You can put this solution on YOUR website!


An easier way to think about it is to look at the probability of
1-(B winning all the time)
Or in other words all the times except where B always wins.
The chance of B winning the first time is 2%2F3. The chance of him winning twice in a row is 4%2F9, because you need to multiply the 2/3's together to reflect them both happening. If they play 5 games, the probability of him winning all the time would be:
2%2F3%2A2%2F3%2A2%2F3%2A2%2F3%2A2%2F3
When you multiply all the numerators and denominators, you get
2%5E5%2F3%5E5
Calculate those numbers, and you get:
32%2F243
The answer, however is 1-32%2F243, or
243%2F243-32%2F243
%28243-32%29%2F243
211%2F243
This is your final answer. If you want a percent, it's ≈86.83%