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A prisoner is given a chance at winning his freedom. He is given a bag that...

A prisoner is given a chance at winning his freedom. He is given a bag that contains 10 black marbles and 10 white marbles. After he is blindfolded, he is to choose 5 marbles. If he draws exactly 3 white marbles he will go free, otherwise he will remain in prison.

He is given the option of replacing the marble after each selection or not replacing the marble after each selection. Which option will give him the best chance of going free? Show all your calculations to justify your answer and clearly explain the main difference between the two scenarios.

Please use binomial and hypergeometric distribution to explain.

Math   Statistics-And-Probability   
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