If Ben were to lose the championship, Mike would be the winner with a probability of $$\dfrac14,$$ and Rob $$-\dfrac13.\ This topic has expert replies Moderator Posts: 1068 Joined: 29 Oct 2017 Thanked: 1 times Followed by:5 members If Ben were to lose the championship, Mike would be the winner with a probability of \(\dfrac14,$$ and Rob $$-\dfrac13.\ by M7MBA » Tue Sep 15, 2020 5:43 am Timer 00:00 Your Answer A B C D E Global Stats If Ben were to lose the championship, Mike would be the winner with a probability of \(\dfrac14,$$ and Rob $$-\dfrac13.$$ If the probability of Ben being the winner is $$\dfrac17,$$ what is the probability that either Mike or Rob will win the championship? Assume that there can be only one winner.

A. $$\dfrac1{12}$$

B. $$\dfrac17$$

C. $$\dfrac12$$

D. $$\dfrac7{12}$$

E. $$\dfrac67$$

Source: GMAT Club Tests

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Re: If Ben were to lose the championship, Mike would be the winner with a probability of $$\dfrac14,$$ and Rob $$-\dfrac by Scott@TargetTestPrep » Thu Sep 24, 2020 7:11 am M7MBA wrote: Tue Sep 15, 2020 5:43 am If Ben were to lose the championship, Mike would be the winner with a probability of \(\dfrac14,$$ and Rob $$-\dfrac13.$$ If the probability of Ben being the winner is $$\dfrac17,$$ what is the probability that either Mike or Rob will win the championship? Assume that there can be only one winner.

A. $$\dfrac1{12}$$

B. $$\dfrac17$$

C. $$\dfrac12$$

D. $$\dfrac7{12}$$

E. $$\dfrac67$$

Source: GMAT Club Tests
Solution:

Since the probability that Ben wins is 1/7, the probability that he loses is 6/7.

P(Mike or Rob wins) = P(Ben loses and Mike wins) + P(Ben loses and Rob wins)
= 6/7 * 1/4 + 6/7 * 1/3 = 3/14 + 2/7 = 3/14 + 4/14 = 7/14 = 1/2