SOLUTION: Can someone help me? Two fair six sided dice are rolled. Find the probability that the faces are different given that the dice show a sum of ten. I got 2/36 because (6,4) (4,6),

Question 1096015: Can someone help me?
Two fair six sided dice are rolled. Find the probability that the faces are different given that the dice show a sum of ten.
I got 2/36 because (6,4) (4,6), but the answer is 2/3. Where am I wrong?
Thank you.
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

There are 6*6 = 36 different outcomes when two dice are rolled. 3 of those outcomes have a sum of 10: 4+6, 5+5, and 6+4.

So let's look at some probabilities related to this....

(1) The probability of getting a 10 when two dice are rolled is 3/36, or 1/12.

(2) The probability of getting a 10 WITH TWO DIFFERENT NUMBERS when two dice are rolled is 2/36, or 1/18. That is the question you answered.

(3) But the probability of getting a 10 with two different numbers, AND GIVEN THAT THE SUM IS 10, is 2/3.

That "given that the sum is 10" means the denominator of your probability fraction is only the total number of ways of getting a sum of 10.

So there are 3 ways of getting a sum of 10, and 2 of those ways have different numbers. So when the problem asks to "find the probability that the faces are different given that the dice show a sum of ten", the answer is 2/3.
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