# Binomial Distribution as a Probability Model

In problems 1 and 2, indicate whether a binomial distribution is a reasonable probability model for the random variable X. Give your reasons in each case.

1. The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty. X is the number who say, "Yes."

2. Joey buys a Virginia lottery ticket every week. X is the number of times in a year that he wins a prize.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

1. Yes, the binomial distribution is appropriate in this case because the probability whether a person supports or opposes the death penalty (0.5 each) remains the same from person to person and every person's opinion is independent of the other's opinions.

2. No, the binomial distribution is not appropriate in this case as the probability of winning the lottery may change from week to week. Suppose 15000 people bought the ticket this week. Then Joey's probability of winning is 1/15,000. If 14,345 people bought the ticket next week, then Joey's probability of winning would be 1/14,345.

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