A box contains 300 blue and 700 red balls. In each of the following items, list

Question

A box contains 300 blue and 700 red balls. In each of the following items, list the possible values that the random variable X can have and and its probability mass function. Which one is a Bernoulli, a Binomial, a Geometric, a Hypergeometric random variable? No need to simplify binomial coefficients in this problem. (a) 200 balls are randomly chosen (without replacement), and X is the number of blue balls chosen. (b) One ball is drawn randomly and then returned. This keeps going on until a blue ball has been drawn. X is how many drawings were necessary. (c) One ball is drawn randomly, its color is noted, and then it is returned. This happens 200 times. X is the number of times it was a blue ball (d) A ball will be selected randomly. If it is blue, you get $1, and if it is red you get nothing. X is the money you will get

Explanation / Answer

a.) This is a case of hypergeometric distribution.

b.) This is a case of geometric distribution.

c.) This is a case of Bernoulli distribution.

d.) This is a case of binomial distribution.

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