dtweah wrote:The probability that amit will qualify in an exam is .05. The probability that anita will qualify is .10. The probability that both will qualify is .02. Find the percent chances of both failing to qualify.
A. 50%
B. 25.5%
C. 37%
D. 53%
E. 87%
This is not a conventional GMAT probability problem. Normally, in similar GMAT probability questions, our events would be completely
independent. When two events are independent, and we want to know the probability both events happen, we just multiply the probability of each event happening. So, if the probabilities here were independent, the probability Amit and Anita would both qualify would just be (0.1)(0.05) = 0.005.
Now, we know that's not the case here, so their probabilities of qualifying must not be independent for some reason - perhaps one of them is copying a few answers from the other's exam paper, which makes their fortunes more intertwined than normal. That fact just turns this into a Venn diagram question. We know that if they take the test 100 times:
* Both will qualify 2 times
* Amit will qualify 5 times, so Amit alone will qualify 3 times
* Anita will qualify 10 times, so Anita alone will qualify 8 times
Thus at least one of them qualifies 2+3+8 = 13 times out of 100, and thus neither qualifies 87 times out of 100.
I've never seen such a question on the GMAT, however.
