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What are the odds of rolling doubles on 3 six-sided dice?
I'm trying to figure out what the probability is of rolling doubles (ie. two of the same number) when you roll 3, six-sided dice.
As the experiment is rolling 3 numbers of six-sided dice,
the number of elements is sample space = 216
Of the three numbers two of them to be same is (1,1) (2,2) (3,3) (4,4) (5,5) (6,6) = 6 doublets
Every one of this can happen in 3 different ways, that is (1,1,x) (1,x,1) (x,1,1) = 3 ways
Now x can be any of the remaining three numbers, that is (2,1,1) (3,1,1) --- = 5
So total number of ways two of them can be same = 6 x 3 x 5 = 90
So probability of the event = 90/216 = 5/12
You may also work out the elements for favorable events in another method:
All the digits are same = 6
Everyone of them is different = 6 x 5 x 4 = 120
Out of 216 rest are two digits are same = 216 - (120 + 6) = 90
==> Probability = 90/216 = 5/12
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