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Is there a way to do this without the binomial probability? Consider the following game: You...

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Basic Math

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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