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Question of the Day: Finite Mathematics

Mike and Spike are playing a game of poker dice, in which a turn comprises the following process:

1) Roll all five dice - note: these are standard six-sided dice, which you may assume to be fair.

2) Keep the dice you want, then roll the remaining dice in hope of improving your score.

3) Repeat Step 2, after which whatever you have stands.

Mike is down to his last turn. He has rolled the dice once and has the following: 1-3-3-3-5.

He must roll a five of a kind in order to score. If he re-rolls the "1" and the "5", what is the probability that he will get five "3's"?

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