What is the probability that at least two of the faces match when you roll three fair six-sided dice? Express your answer as a common fraction.
This seems easy, but the *at least* makes it harder, all I understand is with the at least you need to subtract a certain probability from 1 xd
First die: Any number
2nd die : probability that it is different from the first = 5/6
3rd die: probability that it is different from the first two dice=4/6
So, the probability of getting a matching pair is:
1 -[6/6 x 5/6 x 4/6]=1 - 120/216 =96/216 = 12/27 = 44.44%
Note: This is the same as getting one particular pair(say 2 ones), which gives you the probability of 2/27. But you have 6 numbers that can be matched as pairs(11, 22, 33, 44, 55, 66). So:2/27 x 6 =12/27 =44.44%