According to the Statistical Abstract of the United States,...

According to the Statistical Abstract of the United States, $70.3 \%$ of females ages 20 to 24 have never been married. Choose 5 young women in this age category at random. Find the probability that
a. None has ever been married
b. At least 1 has been married

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Key Concepts

Binomial Distribution

The binomial distribution is a probability distribution that expresses the probability of a given number of successes in a fixed number of independent trials, each with the same probability of success. In this context, each young woman's marital status is considered an independent trial with the probability of not being married (or being married) determining success.

Bernoulli Trials

Bernoulli trials are experiments or processes that result in one of two outcomes, often labeled as “success” and “failure”. Here, each selection of a young woman can be seen as a Bernoulli trial where the outcomes are binary: either she has never been married or she has been married.

Complement Rule

The complement rule is a fundamental principle in probability stating that the probability of an event occurring is equal to one minus the probability of it not occurring. This rule is especially useful when calculating the probability of at least one success, by subtracting the probability of zero successes from one.

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