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# A question I am confused about:

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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.

Jan 30, 2019

#1
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$$P[\text{at least 2 match}]=\\ 1-P[\text{none match}] = \\ 1-\dfrac{\dbinom{6}{3}3!}{6^3} = \\ 1 -\dfrac 5 9 = \\ \dfrac 4 9$$

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Jan 30, 2019
#2
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Here's another way to see this

P(at least two match)  =     1 - P(that none match)

Note....that for none to match....the first die has 6/6 a chance of showing any number.....the second has a 5/6 chance of not showing the first number...and the third die has a 4/6 chance of not showing either of the first two numbers

So....P(none to match)  =  (6/6)(5/6)(4/6)  = 20/36  = 5/9

So....P (at least two match)  =  1 - 5/9   =  4/9

Jan 30, 2019