Hypergeometric Distribution Binomial experiments require that any sampling be done with replacement because each trial must be independent of the others. The hypergeometric distribution also has two outcomes: success and failure. The sampling, however, is done without replacement. For a population of N items having k successes and failures, the probability of selecting a sample of size that has successes and failures is given by



In a shipment of 15 microchips, 2 are defective and 13 are not defective. A sample of three microchips is chosen at random. Use the above formula to find the probability that (c) two microchips are defective and one is not defective.

In Exercises 1–3, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

One out of every 42 tax returns for incomes over $1 million requires an audit. An auditor is examining tax returns for over $1 million. Find the probability that (b) the first return requiring an audit is the first or second return the tax auditor examines, 

In Exercises 1–3, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.

One out of every 42 tax returns for incomes over $1 million requires an audit. An auditor is examining tax returns for over $1 million. Find the probability that (c) none of the first five returns the tax auditor examines require an audit.

Hypergeometric Distribution Binomial experiments require that any sampling be done with replacement because each trial must be independent of the others. The hypergeometric distribution also has two outcomes: success and failure. The sampling, however, is done without replacement. For a population of N items having k successes and failures, the probability of selecting a sample of size that has successes and failures is given by

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In a shipment of 15 microchips, 2 are defective and 13 are not defective. A sample of three microchips is chosen at random. Use the above formula to find the probability that (a) all three microchips are not defective

Hypergeometric Distribution Binomial experiments require that any sampling be done with replacement because each trial must be independent of the others. The hypergeometric distribution also has two outcomes: success and failure. The sampling, however, is done without replacement. For a population of N items having k successes and failures, the probability of selecting a sample of size that has successes and failures is given by

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In a shipment of 15 microchips, 2 are defective and 13 are not defective. A sample of three microchips is chosen at random. Use the above formula to find the probability that (b) one microchip is defective and two are not defective

In Exercises 11 and 12, determine whether the experiment is a binomial experiment. If it is, identify a success; specify the values of n, p, and q; and list the possible values of the random variable x. If it is not a binomial experiment, explain why.

A fair coin is tossed repeatedly until 15 heads are obtained. The random variable x counts the number of tosses.

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.

Fifty-three percent of U.S. adults support attempting to land an astronaut on Mars. You randomly select eight U.S. adults. Find the probability that the number who support attempting to land an astronaut on Mars is (a) exactly three

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.

Fifty-three percent of U.S. adults support attempting to land an astronaut on Mars. You randomly select eight U.S. adults. Find the probability that the number who support attempting to land an astronaut on Mars is (b) at least three

In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B.

Fifty-three percent of U.S. adults support attempting to land an astronaut on Mars. You randomly select eight U.S. adults. Find the probability that the number who support attempting to land an astronaut on Mars is (c) more than three.