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Old 08-02-2002, 08:06 AM
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Default Re: Don\'t Use Formula For This

For a given throw to have exactly 1 three, any of the 5 dice can have the three, and the other 4 dice can have any of 5 remaining numbers, so there are 5*5^4 ways for the throw to have exactly one 3. The total number of ways to throw 5 dice is 6^5, so the probability on one throw is 5*5^4/6^5 = 40%.

Now there is a 60% probability of NOT getting exactly 1 three on any throw, so the probability of getting it on the first throw and not on the next 4 is .4(.6)^4 = 5.2%. But since we can get it on any of the 5 throws we multiply this by 5 to get 26%.
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