Probability of Pairs of Draws

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S = {2, 3, 4, 6}

T = {2, 3, 4, 6}

Two integers will be randomly selected from the sets above, one integer from set S and one integer from set T. What is the probability that the product of the two integers will equal 12?

Review: Probability of Pairs of Draws


Explanation

In this question, we can start with the draw from Set S and imagine the case in which the draw is a 2. In this case, the product of the S draw and the T draw will be 12 only if the T draw is 6, and there is a possibility of that T draw. Imagining another case, if the S draw is 3, the T draw must be 4. Again, a possibility. Indeed, the probability is in any case, so the correct answer is (C).

Consider this variation: What if there's no set T at all, and we want to know the probabilities if there are two distinct draws from Set S? If the draws must be distinct, then in the case in which we draw a 2, there are only three numbers left, so the probability of drawing a 6 is . The probability is in all cases and is the answer to that variation on the question.

Another variation: What if set T has a 5 rather than a 6? Then the probability is not the same in all cases: it's zero if we draw a 2 from set S, and it's in the other cases. The expected value in this variation is .

Again, in this question, the correct answer is (C).


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