You have a bowl with 6 red, 6 black, and 6 green jelly beans. You take 4 jelly b

Question

You have a bowl with 6 red, 6 black, and 6 green jelly beans. You take 4 jelly beans from the bowl. X is the number of black jelly beans selected in 4 draws. 1. if you do this experiment without replacing the jelly beans after each draw.....why would x not be a binomial random variable? 2. if you do this experiment and DO replace the jelly beans after each draw.....why would x be a binomial random variable? You have a bowl with 6 red, 6 black, and 6 green jelly beans. You take 4 jelly beans from the bowl. X is the number of black jelly beans selected in 4 draws. 1. if you do this experiment without replacing the jelly beans after each draw.....why would x not be a binomial random variable? 2. if you do this experiment and DO replace the jelly beans after each draw.....why would x be a binomial random variable?

Explanation / Answer

1) If the selection is done without replacement, then the trials will not be independent, thus not a binomial random variable. That is, the 1st selection will impact the probabiltiy of the next selection being black, and the 2nd selection will impact the proability of the 3rd selection being black, and so on... One of the conditions for a binomial random variable is that the probability of success (in this case selecting black) stays the same from trial to trial. 2) If the selection is done with replacement, the the trials are independent, thus it is a binomial random variable. The probability of black will be the same for each trial 6/18 = 1/3

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