The probability that Mike can win is 1/4, Rob winning is

Question

The probability that Mike can win is 1/4, Rob winning is 1/3, Ben winning is 1/6. What is the probability that mike or rob will win but NOT Ben.

1/6
5/12
7/12
5/6
1

kapslock · Answer

Am I making a mistake? 

Probability that Mike OR Rob wins is 1/4 + 1/3 = 7/12.
Probability that Ben does NOT win = 5/6.
Thus probability that Mike or Rob wins, and Ben does not = 35/72.

yach · Answer

This question is from a GMAT Challenge test. I got the same answer as you but the computer said it was 5/12. I just want to confirm that we have the right answer.

gmatacer · Answer

yeah I can't reach any other answer

vipin7um · Answer

There are 3 scenarios

MR(B)
M(R)(B)
(M)R(B)

where A - Probability of A winning
and (A) - Probability of A not winning

=> 1/4*1/3*5/6 + 1/4*2/3*5/6 + 3/4*1/3*5/6 = 5/12

- Vipin

MA466 · Answer

I also agree with Kpslock anser explanation

MA466 · Answer

Vipin,
Could you please explain your answer? I did not unsderstand your answer. Thanks
ma466

vipin7um · Answer

There are 3 scenarios. Either Mike and Rob will win, or only Mike will win, or only Rob will win.

p(M wins) = 1/4 => p(M doesn't win) = 3/4
p(R wins) = 1/3 => p(R doesn't win) = 2/3
p(B wins) = 1/6 => p(B doesn't win) = 5/6

Scenario1 - 
p(M wins) * p(R wins) * p(B doesn't win) + 

Scenario2
p(M wins) * p(R doesn't win) * p(B doesn't win) + 

Scenario3
p(M doesn't win) * p(R wins) * p(B doesn't win)

This is what the above expression represents.

HTH...

Thanks,
Vipin

giddi77 · Answer

Good explanatio Vipin. I also fell into the trap :wall

MA466 · Answer

Hi Vipin,
Thanks for your explanation but we need scenario 1 based on the question. Why do we need to consider rest of the scenarios i mean 2and3?

ma466

vipin7um · Answer

Hi MA,
Actually question says Mike  OR  Rob should win and Bob shouldn't win. Had it been Mike  AND  Rob should win, then we would have considered only Scenario1.

rambler · Answer

Hi! I am newbie - both to gmat and this forum.. i arrived at the solution like this:

(1/4 + 1/3) - 1/6

which is 5/12

The answers seems correct but what about the approach?

ccax · Answer

Well, it's interesting that you arrived at the correct solution, but I fear you were lucky :-D

First event: The probability that Ben doesn't win is 1-1/6 = 5/6 Second event: The probability that Mike or Rob wins is 1/4 + 1/3 - (1/4 * 1/3) = 1/2 So the answer is 5/6 * 1/2 = 5/12. Those of you who got 35/72 forgot to subtract 1/3 * 1/4 from the addition Mike and Rob. This has to be done because this part has been counted twice. Just consider two events with probability 0.8 that are independent. The probability that at least one of those occurs is 0.8 + 0.8 - 0.8*0.8 = 0.96 (and of course not 1.6).

sherinaparvin · Answer

I have nothing more to add to ccax post. I also arrive to the solution in the same way.

(P(M) + P(R) - P(M)(R)) * P(not B) = 5/12

M8 · Answer

Great explanation ccax .

The probability that Mike can win is 1/4, Rob winning is

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