# Two dice are rolled. Find the probability that the faces are different given that the dice show sum of 10?

Here are the list of equally likely outcomes that have sum of 10.

4 + 6 = 10 5 + 5 = 10 6 + 4 = 10

Out of these 3, only two outcomes are those that have different faces (first and last).

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To find the probability that the faces of two dice are different given that the sum of the dice is 10, first, we determine the possible combinations of rolls that result in a sum of 10. These combinations are (4, 6) and (6, 4).

Out of these combinations, only one of them has different faces, namely (4, 6) or (6, 4).

Therefore, the probability that the faces of the two dice are different given that the sum is 10 is 1 out of 2, or 1/2.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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