Friday, November 26, 2010

CP #19

If Ben were to lose the championship, Mike would be the winner with a probability of [m]\frac{1}{4}[/m] , and Rob - [m]\frac{1}{3}[/m] . If the probability of Ben winning is [m]\frac{1}{7}[/m] , 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]
  • [m]\frac{1}{12}[/m]
  • [m]\frac{1}{7}[/m]
  • [m]\frac{1}{2}[/m]
  • [m]\frac{7}{12}[/m]
  • [m]\frac{6}{7}[/m]
The probability of Mike or Rob winning, conditional on Ben losing, is [m]\frac{1}{4} + \frac{1}{3}[/m] or [m]\frac{7}{12}[/m] . The unconditional probability (to take into consideration the probability of Ben winning) is then [m](1-\frac{1}{7}) * \frac{7}{12} = \frac{6}{7} * \frac{7}{12} = \frac{1}{2}[/m] .
The correct answer is C.
I have calculated it very differently and gotten 5/14 for an answer.

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