# The probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 8?

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I’m not sure what this problem means. If the sum of the dice is 8, does that mean the highest sides add up to 8, therefore each would be four since it is [fair] dice?

• The fair dice part just means that there is an equal probability that each die lands on any number, not that they have to be the same.

The ways that dice can add up to be 8 are: 4 & 4, 3 & 5, and 2 & 6. There is only way they can be 4 & 4( each die is a 4), and there are two ways for 3 & 5 and 2 & 6.

So, there are five possible ways that the dice could add up to 8, and two of these have a 5 showing, so your probability is 2/5.

• There are five combinations with a sum of 8: 6-2, 5-3, 4-4, 3-5, 2,6. If the dice have already landed, then there are two chances out of the five that one of the dice will be a five. 2/5. (You never read the sides of dice under ordinary circumstances, just the tops.)

• There are only 5 possibilities of getting 8 as sum:

(2,6)(3,5)(4,4)(5,3)(6,2)

As the dices are fair, there are total 36 possible outcomes.

So, no. of favorable outcomes with sum of dices as 8 and 5 on one of them=2

Thus, probability=2/36=1/18

• Given that the sum is 8 means that the sum is 8. So instead of 36 possibilities, we are now limited to the following:

2,6

3,5

4,4

5,3

6,2

So total outcomes (given that sum is 8) = 5

In 2 cases, a 5 is present.

Probability = 2/5 = 0.4

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