+1206 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?
+6248 \(\text{Since you are replacing the marbles after each draw the total number of green marbles}\\ \text{you select has a binomial distribution with parameters }n=5,~p=\dfrac 3 5\\ \)
\(P[2] = \dbinom{5}{2} \left(\dfrac 3 5\right)^2 \left(\dfrac 2 5\right)^3 = \dfrac{144}{625}\)
.+6248 \(\text{Since you are replacing the marbles after each draw the total number of green marbles}\\ \text{you select has a binomial distribution with parameters }n=5,~p=\dfrac 3 5\\ \)
\(P[2] = \dbinom{5}{2} \left(\dfrac 3 5\right)^2 \left(\dfrac 2 5\right)^3 = \dfrac{144}{625}\)
