SOLUTION: Four marbles are selected, one at a time from a bin of marbles containing 6 black, 6 red and 6 green marbles. Let x represent the number of green marbles drawn in 4 draws. (A)

Question 477685: Four marbles are selected, one at a time from a bin of marbles containing 6 black, 6 red and 6 green marbles. Let x represent the number of green marbles drawn in 4 draws.

(A) If this experiment is completed without replacing the marbles, explain why x is not a binomial random variable.
(B) If this experiment is completed with replacement of the marbles, explain why x is a binomial random variable.

Thank your for your help

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
(A) If without replacement, X is not a binomial random variable, because the probability p for should not change after after every trial. The change in the value of p comes from the lack of independence of the trials due to non-replacement.
(B) If there is replacement, then the trials are independent, and the probability of getting a green marble is 6/18 = 1/3 throughout the experiment.
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