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):
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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