Two marbles are selected, one at a time from a jar of marbles containing 10 black, 10 brown, 10 white and 10 green marbles. Let x represent the number of white marbles selected in 2 separate selections from the jar.
(A) If this experiment is completed without replacing the marbles each time, explain why x is not a binomial random variable.
(B) If this experiment is completed with replacement of the marbles each time, explain why x is a binomial random variable.
a) By removing a marble and not replacing it, the trials are no longer independent (there is a change in probability from one trial to the next). This condition must be satisfied if x is considered to be a binomial random variable.
b) Because there is sampling with ...
This solution (including over 150 words) provides explanations for two questions specific to a probability example involving marbles.