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06 Mar 2015, 07:24
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A
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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.
(1) n > 3
(2) n < 6
Kudos for a correct solution.
08 Mar 2015, 16:21
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Bunuel
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.
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gdspqop_img2.png [ 4.85 KiB | Viewed 13954 times ]
Suppose n = 3.
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gdspqop_img3.png [ 4.94 KiB | Viewed 13948 times ]
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.
General Discussion
06 Mar 2015, 09:15
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Probability of at least once is 1 - probability of not happening at all.
n=1>>=1- (1/4)=3/4=0.75
n=3>>=(1- (1/4))^3=0.42
n=4>>=(1- (1/4))^4=.31
statement 1 will have always have values smaller than .5 so sufficient
statement 1 will have values smaller and larger than .5 so insufficient
answer is A
n=1>>=1- (1/4)=3/4=0.75
n=3>>=(1- (1/4))^3=0.42
n=4>>=(1- (1/4))^4=.31
statement 1 will have always have values smaller than .5 so sufficient
statement 1 will have values smaller and larger than .5 so insufficient
answer is A
