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John has seven red marbles and three blue marbles in a bag. He removes a marble at random, records the color, puts it back, and then repeats this process until he has withdrawn six marbles. What is the probability that exactly three of the marbles that he removes are red? Express your answer as a decimal rounded to the nearest thousandth.

Also an explanation is more helpful than just an answer, I would appreciate it if you took the extra time to help :)

 Jun 29, 2021
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7/10 * 7/10 * 7/10 * 3/10 * 3/10 * 3/10

red * red * red * blue * blue * blue

 

This equals 9261/1000000

 

But we also have to account for the cases for arranging

there are 6!/3! * 3! ways to arrange each of these, so

9261/1000000 * 20 = 0.18522, or 0.185 

 Jun 29, 2021

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