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The probability that an event A occurs is 1/2 and the probability that

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Math Revolution GMAT Instructor
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The probability that an event A occurs is 1/2 and the probability that  [#permalink]

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New post 08 Nov 2017, 23:38
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[GMAT math practice question]

The probability that an event A occurs is 1/2 and the probability that an even B occurs is 1/3. If event A and event B are independent, what is the probability that event A occurs but event B does not occur?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6

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Math Revolution GMAT Instructor
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Re: The probability that an event A occurs is 1/2 and the probability that  [#permalink]

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New post 09 Nov 2017, 00:00
1
=>

Since events A and B are independent, P(A∩B) = P(A) ∙P(B).
The probability P(A-B) = P(A) - P(A∩B) = P(A) - P(A) ∙P(B) = 1/2 – (1/2)(1/3) = 1/2 – 1/6 = 2/6 = 1/3.

Thus, the answer is B.
Answer: B
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Re: The probability that an event A occurs is 1/2 and the probability that  [#permalink]

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New post 12 Nov 2017, 07:47
1
MathRevolution wrote:

The probability that an event A occurs is 1/2 and the probability that an even B occurs is 1/3. If event A and event B are independent, what is the probability that event A occurs but event B does not occur?

A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6


The probability that event B does not occur is 1 - 1/3 = 2/3.

Since we want the probability that A occurs AND that B does not occur, we multiply their respective probabilities. Thus, the probability that event A occurs but event B does not occur is 1/2 x 2/3 = 1/3.

Answer: B
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Re: The probability that an event A occurs is 1/2 and the probability that  [#permalink]

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New post 21 Dec 2017, 01:34
MathRevolution wrote:
=>

Since events A and B are independent, P(A∩B) = P(A) ∙P(B).
The probability P(A-B) = P(A) - P(A∩B) = P(A) - P(A) ∙P(B) = 1/2 – (1/2)(1/3) = 1/2 – 1/6 = 2/6 = 1/3.

Thus, the answer is B.
Answer: B



Dear instructor, could you be so kind to explain that \(P(A-B) = P(A) - P(A∩B)\) actually means. I know that in a Venn diagram \(A∩B\) means itersection but I can't figure out how it works for our problem. Thanks
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Re: The probability that an event A occurs is 1/2 and the probability that &nbs [#permalink] 21 Dec 2017, 01:34
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The probability that an event A occurs is 1/2 and the probability that

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