jmc

Question

Phil has 7 green marbles and 3 purple 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 He removes a marble at random, records the color, puts it back, and then repeats this process until he has withdrawn 6 marbles. What is the probability that exactly three of the marbles that he removes are green? Express your answer as a decimal rounded to the nearest thousandth.

Accepted Answer

There is a ( 710 ) ^3 ( 310 ) ^3 = 92611000000 probability that 3 particular marbles out of 6 will be green and the rest will be purple. There are also 63=20 ways to choose which 3 out of the 6 are the green ones. Because these ways are all mutually exclusive, we multiply to get the probability that we're looking for: 20 92611000000 .185.