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What is the probability that at least two of the faces match when you roll four fair six-sided dice? Express your answer as a common fraction.

 Feb 14, 2022
 #1
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The probability is 23/216.

 Feb 14, 2022
 #2
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First die, any number==6/6

2nd die, probability that it is different fron the first==5/6

3rd die, probability that it is different from the first two ==4/6

4th die, probability that it is different from the first three ==3/6

 

Then, the overall probability that they are all different from each other==6/6 x 5/6 x 4/6 x 3/6==360 / 6^4

 

Therefore, the probability that at least 2 of them are the same==1 - [360 /1,296] ==13 /18 ==72.22%

 Feb 14, 2022

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