SOLUTION: Three 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 black marbles drawn in 3 draws. (A

Question 610377: Three 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 black marbles drawn in 3 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.

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,

Three 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 black marbles drawn in 3 draws.

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

trials are NOT of one another and P(black) is different for each trial

(B) If this experiment is completed with replacement of the marbles, explain why x is a binomial random variable.

Satisfies all of the below.

______________________________________________________________________________

A binomial experiment (also known as a Bernoulli trial) is a statistical experiment that has the following properties:

■The experiment consists of n repeated trials.

■ Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.

■ The probability of success, denoted by P, is the same on every trial.

■ The trials are ; that is, the outcome on one trial does not affect the outcome on other trials.

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