According to a recent survey, 81 percent of adults in a certain state have graduated from high school. If 15 adults from the state are selected at random, what is the probability that 5 of them have not graduated from high school?

A. \(\frac{20}{50}\) \((0.19)^{15}(0.81)^{5}\)

B. \(\frac{10}{50}\) \((0.19)^{15}(0.81)^{5}\)

C. \(\frac{20}{50}\) \((0.81)^{5}(0.19)^{10}\)

D. \(\frac{20}{50}\) \((0.81)^{5}(0.19)^{10}\)

The correct formula from the given options for computing probability of exactly 5 out of randomly chosen 15 adults not being high school graduates is option c.) (20/50) (0,81)⁵(0,19)¹⁰

Explanation:

The question is asking about the probability of selecting a specific number of adults who have not graduated high school from a randomly chosen sample.

Given that 81% of adults have graduated high school, it indicates that 19% (or 0.19 as a probability) have not graduated.

This problem is an example of a binomial probability problem.

Binomial probability can be calculated as:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

Which means we want exactly 'k' successes (some specific number of people in our group) out of 'n' trials (total selected number), where 'p' is the probability of a single success (a person not having a high school diploma).

Following these notations: here n=15 (randomly selected adults), k=5 (people who haven't graduated), and p=0.19 (probability of one adult not having a high school degree).

The answer will be the selection of correct formula from the options given: . (20/50) (0,81)⁵(0,19)¹⁰

Learn more about Binomial probability here:

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