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What is the probability of getting at least one pair if four fair six sided dice are rolled simultaneously?
Cant this question be thought of as 1- (Probability of getting 0 pairs)??
Complementary?
P= 1- (1 * (5/6) * (4/6) * (3/6) ) = (6^3 - 60) / (6^3)
Correct? Essentially each result on each roll should be different.
But why if I solve the problem using the alternative method (solving each case individually) do I obtain a different answer.
so:
you can either have 1 pair or 2 pairs if you roll a dice 4 times. A (3,3,3,4) would still only count as one pair, in my opinion. please tell me if I am wrong.
using this logic, since we want to know probability of 1 pair OR 2 pairs:
1 pair = (1* 1/6 * 1 * 5/6)
2 pair = (1 * 1/6 * 1 * 1/6)
P = 5/36 + 1/36 = 1/6
I dont understand.
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