Question 858001
 
 
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 {{{2/3}}}. The chance of him winning twice in a row is {{{4/9}}}, 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:
{{{2/3*2/3*2/3*2/3*2/3}}}
When you multiply all the numerators and denominators, you get
{{{2^5/3^5}}}
Calculate those numbers, and you get:
{{{32/243}}}
The answer, however is 1-{{{32/243}}}, or
{{{243/243-32/243}}}
{{{(243-32)/243}}}
{{{211/243}}}
This is your final answer. If you want a percent, it's ≈86.83%