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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