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. \(\dfrac67\)
Answer: C
Source: GMAT Club Tests
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If Ben were to lose the championship, Mike would be the winner with a probability of \(\dfrac14,\) and Rob \(-\dfrac13.\
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Solution:M7MBA wrote: ↑Tue Sep 15, 2020 5:43 amIf 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. \(\dfrac67\)
Answer: C
Source: GMAT Club Tests
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
Answer: C
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