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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
Joined: 16 Aug 2015
Posts: 4863
GPA: 3.82
The probability that an event A occurs is 1/2 and the probability that [#permalink]

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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
[Reveal] Spoiler: OA

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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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09 Nov 2017, 00:00
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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.

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

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12 Nov 2017, 07:47
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Expert's post
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.

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

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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.

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
Re: The probability that an event A occurs is 1/2 and the probability that   [#permalink] 21 Dec 2017, 01:34
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