Is there a way to do this without the binomial probability?
Consider the following game: You roll six 6-sided dice d1,…,d6and you win if some number appears 3 or more times. For example, ifyou roll:
(3,3,5,4,6,6)
then you lose. If you roll
(4,1,3,6,4,4)then you win.
What is the probability that you win this game?
The answer is 119/324
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