## Friday, November 26, 2010

### CP #19

If Ben were to lose the championship, Mike would be the winner with a probability of $\frac{1}{4}$ , and Rob - $\frac{1}{3}$ . If the probability of Ben winning is $\frac{1}{7}$ , what is the probability that either Mike or Rob will win the championship (there can be only one winner)?
(C) 2008 GMAT Club - [t]m07#12[/t]
• $\frac{1}{12}$
• $\frac{1}{7}$
• $\frac{1}{2}$
• $\frac{7}{12}$
• $\frac{6}{7}$
The probability of Mike or Rob winning, conditional on Ben losing, is $\frac{1}{4} + \frac{1}{3}$ or $\frac{7}{12}$ . The unconditional probability (to take into consideration the probability of Ben winning) is then $(1-\frac{1}{7}) * \frac{7}{12} = \frac{6}{7} * \frac{7}{12} = \frac{1}{2}$ .