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The probability that event A occurs is 1/3, and the probability that e

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MathRevolution
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The probability that event A occurs is 1/3, and the probability that e [#permalink] New post   09 Feb 2018, 01:44
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[GMAT math practice question]

The probability that event A occurs is \(\frac{1}{3}\), and the probability that event B occurs is \(\frac{1}{12}\). If events A and B are independent, what is the probability that both events A and B occur?

\(A. \frac{1}{6}\)
\(B. \frac{1}{12}\)
\(C. \frac{1}{15}\)
\(D. \frac{1}{18}\)
\(E. \frac{1}{36}\)
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Re: The probability that event A occurs is 1/3, and the probability that e [#permalink] New post   11 Feb 2018, 18:01
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If events A and B are independent, then \(P(A∩B) = P(A)P(B)\).
So, \(P(A∩B) = P(A)P(B) = \frac{(1}{3)}*\frac{(1}{12)} = \frac{1}{36}.\)

Therefore, the answer is E.

Answer : E
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Re: The probability that event A occurs is 1/3, and the probability that e [#permalink] New post   09 Feb 2018, 02:06
MathRevolution wrote:
[GMAT math practice question]

The probability that event A occurs is \(\frac{1}{3}\), and the probability that event B occurs is \(\frac{1}{12}\). If events A and B are independent, what is the probability that both events A and B occur?

\(A. \frac{1}{6}\)
\(B. \frac{1}{12}\)
\(C. \frac{1}{15}\)
\(D. \frac{1}{18}\)
\(E. \frac{1}{36}\)


Probability of both events A and B to occur = P(A) x P(B) = \(\frac{1}{3}\) x \(\frac{1}{12}\)
= \(\frac{1}{36}\)

Answer E.
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Re: The probability that event A occurs is 1/3, and the probability that e [#permalink] New post   12 Feb 2018, 17:35
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MathRevolution wrote:
[GMAT math practice question]

The probability that event A occurs is \(\frac{1}{3}\), and the probability that event B occurs is \(\frac{1}{12}\). If events A and B are independent, what is the probability that both events A and B occur?

\(A. \frac{1}{6}\)
\(B. \frac{1}{12}\)
\(C. \frac{1}{15}\)
\(D. \frac{1}{18}\)
\(E. \frac{1}{36}\)



When two events are independent, we simply multiply their respective probabilities together to determine the probability that both events will happen.

Thus, the probability that both events occur is 1/3 x 1/12 = 1/36.

Answer: E
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Re: The probability that event A occurs is 1/3, and the probability that e [#permalink] New post   10 Dec 2023, 19:11
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Re: The probability that event A occurs is 1/3, and the probability that e [#permalink]
10 Dec 2023, 19:11
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