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06 Mar 2015, 07:25
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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43% (01:23) correct
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Suppose A and B are two events that are not independent. Is the probability P(A and B) > 1/3?
(1) P(A) = 0.8 and P(B) = 0.7
(2) P(A or B) = 0.9
(1) P(A) = 0.8 and P(B) = 0.7
(2) P(A or B) = 0.9
06 Mar 2015, 22:56
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Answer should be A.
P(A U B) = P(A) + P(B) - P(A and B)
option A : P(A U B) = 0.8 + 0.7 - P(A and B) = 1.5 - P(A and B).
P(A U B) can not have value greater than 1, so, P(A and B) >= 0.5. Sufficient.
option B : Clearly Not Sufficient.
P(A U B) = P(A) + P(B) - P(A and B)
option A : P(A U B) = 0.8 + 0.7 - P(A and B) = 1.5 - P(A and B).
P(A U B) can not have value greater than 1, so, P(A and B) >= 0.5. Sufficient.
option B : Clearly Not Sufficient.
08 Mar 2015, 16:14
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Bunuel
MAGOOSH OFFICIAL SOLUTION:
Statement #1: this is very tricky. There is no cut-and-dry probability rule for this. we have to think about overlap. The total probability space, which encompasses anything that possibly could happen, has a size of 1, and P(A) and P(B) have to fit in this space. These two have a size of 0.8 and 0.7 respectively, so they are going to overlap. Think about it visually —
Attachment:
gdspqop_img4.png [ 5.18 KiB | Viewed 23232 times ]
Push the P(A) = 0.8 all the way to the left (whatever that means!), leaving the 0.2 outside of A on the right. Now, push P(B) = 0.7 all the way to the right, leaving the 0.3 outside of B on the left. Suppose the 0.2 outside of A is inside B, and the 0.03 outside of B is inside A. This would be the minimum possible overlap, and even then the overlap, P(A and B), equals 0.5. Thus, P(A and B) ≥ 0.5, so it must be greater than 1/3. this statement allows us to give a definitive answer to the prompt question. This statement, alone and by itself, is sufficient.
Statement #2: forget everything we learned in the analysis of statement (1). Now, all we know is P(A or B) = 0.9, and we know absolutely nothing about P(A) or P(B). We can calculate nothing else. This statement, alone and by itself, is insufficient.
First sufficient, second not sufficient.
Answer = A.
