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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?

 Dec 7, 2018

Best Answer 

 #1
avatar+5172 
+2

\(\text{Since you are replacing the marbles after each draw the total number of green marbles}\\ \text{you select has a binomial distribution with parameters }n=5,~p=\dfrac 3 5\\ \)

 

\(P[2] = \dbinom{5}{2} \left(\dfrac 3 5\right)^2 \left(\dfrac 2 5\right)^3 = \dfrac{144}{625}\)

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 Dec 7, 2018
 #1
avatar+5172 
+2
Best Answer

\(\text{Since you are replacing the marbles after each draw the total number of green marbles}\\ \text{you select has a binomial distribution with parameters }n=5,~p=\dfrac 3 5\\ \)

 

\(P[2] = \dbinom{5}{2} \left(\dfrac 3 5\right)^2 \left(\dfrac 2 5\right)^3 = \dfrac{144}{625}\)

Rom Dec 7, 2018

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