SOLUTION: A fair pair of dice is rolled and the sum of the points is noted. What is the probability that one of the dice results in a point of 6​, given that the sum of the points is 8​?

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Question 1137021: A fair pair of dice is rolled and the sum of the points is noted. What is the probability that one of the dice results in a point of 6​, given that the sum of the points is 8​?
Answer by greenestamps(13200) About Me  (Show Source):
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The sample space for the problem is all the outcomes where the sum of the two dice is 8; the "good" outcomes are the ones that have a 6 on one of the two dice.

6+2
5+3
4+4
3+5
2+6

There are 5 ways to get a sum of 8; 2 of those ways have 6 on one of the two dice.

The probability that one of the dice shows 6, given that the sum of the two dice is 8, is 2/5.

Using the formal mathematical definition of conditional probability....
P(one of the dice is 6 | the sum of the two dice is 8)

= P((one of the dice is 6) AND (the sum of the dice is 8))    2/36     2
  -------------------------------------------------------- = ------ = ---
               P(sum of the dice is 8)                        5/36     5