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jmc

counting and probability intermediate

Problem

John has 6 green marbles and 4 purple marbles. He chooses a marble at random, writes down its color, and then puts the marble back. He performs this process 5 times. What is the probability that he chooses exactly two green marbles?
Solution
There are ways to choose which two of the five marbles John chose were green. For any of those 10 choices, there is a chance for that choice to happen. The total probability is then .
Final answer
\frac{144}{625}