document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #517059 by ben720(159) $\"\"$ $\"About$

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\n" ); document.write( "An easier way to think about it is to look at the probability of
\n" ); document.write( "1-(B winning all the time)
\n" ); document.write( "Or in other words all the times except where B always wins.
\n" ); document.write( "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:
\n" ); document.write( " $\"2%2F3%2A2%2F3%2A2%2F3%2A2%2F3%2A2%2F3\"$
\n" ); document.write( "When you multiply all the numerators and denominators, you get
\n" ); document.write( " $\"2%5E5%2F3%5E5\"$
\n" ); document.write( "Calculate those numbers, and you get:
\n" ); document.write( " $\"32%2F243\"$
\n" ); document.write( "The answer, however is 1- $\"32%2F243\"$ , or
\n" ); document.write( " $\"243%2F243-32%2F243\"$
\n" ); document.write( " $\"%28243-32%29%2F243\"$
\n" ); document.write( " $\"211%2F243\"$
\n" ); document.write( "This is your final answer. If you want a percent, it's ≈86.83%
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