Question 1137021
<br>
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.<br>
6+2
5+3
4+4
3+5
2+6<br>
There are 5 ways to get a sum of 8; 2 of those ways have 6 on one of the two dice.<br>
The probability that one of the dice shows 6, given that the sum of the two dice is 8, is 2/5.<br>
Using the formal mathematical definition of conditional probability....<br><pre>
P(one of the dice is 6 | the sum of the two dice is 8)<br>
= 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</pre>