If Ben were to lose the championship, Mike would be the winner with a probability of ![[m]\frac{1}{4}[/m]](http://gmatclub.com/cgi-bin/mimetex.cgi?%5Cfrac%7B1%7D%7B4%7D)
, and Rob - ![[m]\frac{1}{3}[/m]](http://gmatclub.com/cgi-bin/mimetex.cgi?%5Cfrac%7B1%7D%7B3%7D)
. If the probability of Ben winning is ![[m]\frac{1}{7}[/m]](http://gmatclub.com/cgi-bin/mimetex.cgi?%5Cfrac%7B1%7D%7B7%7D)
, what is the probability that either Mike or Rob will win the championship (there can be only one winner)?
The probability of Mike or Rob winning, conditional on Ben losing, is ![[m]\frac{1}{4} + \frac{1}{3}[/m]](http://gmatclub.com/cgi-bin/mimetex.cgi?%5Cfrac%7B1%7D%7B4%7D%20%2B%20%5Cfrac%7B1%7D%7B3%7D)
or ![[m]\frac{7}{12}[/m]](http://gmatclub.com/cgi-bin/mimetex.cgi?%5Cfrac%7B7%7D%7B12%7D)
. The unconditional probability (to take into consideration the probability of Ben winning) is then  * \frac{7}{12} = \frac{6}{7} * \frac{7}{12} = \frac{1}{2}[/m]](http://gmatclub.com/cgi-bin/mimetex.cgi?%281-%5Cfrac%7B1%7D%7B7%7D%29%20%2A%20%5Cfrac%7B7%7D%7B12%7D%20%3D%20%5Cfrac%7B6%7D%7B7%7D%20%2A%20%5Cfrac%7B7%7D%7B12%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
.
The correct answer is C.
I have calculated it very differently and gotten 5/14 for an answer.
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