Bunuel wrote:
In a single Epsilon trial, the probability of Outcome T is 1/4. Suppose a researcher conducts a series of n independent Epsilon trials. Let P = the probability that Outcome T occurs at least once in n trials. Is P > 1/2?
(1) n > 3
(2) n < 6
Kudos for a correct solution.
MAGOOSH OFFICIAL SOLUTION:So, let’s play with this scenario first a little. Remember, we calculate the “at least” scenario using the complement rule.
Suppose n = 1. Then the probability that T happens at least once (ie. at all!) is 1/4. Of course, this is less than 1/2.
Suppose n = 2.
Attachment:
gdspqop_img2.png [ 4.85 KiB | Viewed 11136 times ]
This probability is just less than 1/2.
Suppose n = 3.
Attachment:
gdspqop_img3.png [ 4.94 KiB | Viewed 11136 times ]
This probability is greater than 1/2.
Now, think about it. As n increases, there are more and more chances for at least one occurrence of T to happen, so as n increase, the probability of at least one T must also increase. Thus, for all values of n greater than 3, the probability will be even higher, so it must be greater than 1/2.
Statement #1: as we just said, for all larger values of n, at long as we are at n = 3 or higher, the answer to the prompt question will be yes. This statement, alone and by itself, is sufficient.
Statement #2: the problem here, if n < 6, then we could have n = 0 or n = 1, in which case the answer to the prompt question is “no”, or we could have n = 3 or higher, in which case the answer is “yes.” Different possible choices give different answers. This statement, alone and by itself, is insufficient.
First sufficient, second not sufficient.
Answer = A.
_________________