A set of ten cards consists of five red cards and five black cards. The cards ar

Question

A set of ten cards consists of five red cards and five black cards. The cards are shuffled thoroughly. Four of these cards will be selected at random without replacement . Let X = the number of red card in the set of Four selected cards. Which of the following probability distributions is appropriate for the random variable X?

A. A continuous distribution with mean 3 and variance 1.22.

B.   A binomial distribution with parameters n = 4 and p = 0.5.

C.   A binomial distribution with parameters n = 10 and p = 0.5.

D. The binomial distribution is inappropriate because the results of trials are not independent.

Explanation / Answer

The distribution is a discrete probability distribution but not binomial.

The outcome of each trial is not independent of the other as the experiment is done without replacemnet. Thus the required answer is:

D. The binomial distribution is inappropriate because the results of trials are not independent.

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