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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
avatar+4789 
+3

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

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 Jan 30, 2019
 #2
avatar+99523 
+2

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

 

cool cool cool

 Jan 30, 2019

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