hey_thr67 wrote:If Ben were to lose the championship, Mike would be the winner with a probability of 1/4, and Rob 1/3. If the probability of Ben being the winner is 1/7, what is the probability that either Mike or Rob will win the championship?
A: 1/12
B: 1/7
C: 1/2
D: 7/12
E: 6/7
Hi, there. I'm happy to help with this.
This is a tricky question. First of all, P(Ben wins) = 1/7, so P(Ben doesn't win) = 1 - 1/7 = 6/7.
The wording of the first part is very important:
If Ben were to lose the championship, Mike would be the winner with a probability of 1/4, and Rob 1/3. This is a conditional probability --- we are told the probability given that a certain condition (Ben losing) is met.
The conditional probability of A, given B, is written P(A|B). The formula for this is
P(A and B) = P(B)*P(A|B)
Here, B = Ben loses, and we want A = Mike or Rob wins.
P(Mike wins|Ben loses) = 1/4
P(Rob wins|Ben loses) = 1/3
Add these two:
P(Mike wins|Ben loses) + P(Rob wins|Ben loses) = P(Mike or Rob wins|Ben loses) = 1/4 + 1/3 = 7/12
P(Mike or Rob wins) = P(Ben loses)*P(Mike or Rob wins|Ben loses) = 6/7 * 7/12 = 6/12 = 1/2
Answer =
C
Again, that was a very hard question. This is at the very outer limit of what the GMAT could possible ask. Here's a much more typical kind of GMAT math probability question.
https://gmat.magoosh.com/questions/1036
When you submit your answer to this question, the next page will have the full video solution.
Let me know if you have any more questions.
Mike
