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A poll is given, showing 80% are in favor of a new building project.

If 3 people are chosen at random, what is the probability that exactly 1 of them favor the new building project?

1 Answer

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Explanation:

To find the probability that exactly 1 out of 3 people chosen at random favor the new building project when 80% are in favor, you can use the binomial probability formula.

The formula for the probability of exactly k successes in n trials, where the probability of success on a single trial is p, is:

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

In this case:

- n (number of trials) is 3.

- k (number of successes) is 1.

- p (probability of success on a single trial) is 0.80 (since 80% are in favor).

Using the formula, you can calculate the probability:

P(X = 1) = (3 choose 1) * (0.80)^1 * (1 - 0.80)^(3 - 1)

P(X = 1) = (3 choose 1) * 0.80 * 0.20^2

You can calculate "3 choose 1" as 3 (it represents the number of ways to choose 1 success out of 3 trials). Now, plug these values into the formula:

P(X = 1) = 3 * 0.80 * 0.20^2

P(X = 1) = 3 * 0.80 * 0.04

P(X = 1) = 0.096

So, the probability that exactly 1 out of 3 people chosen at random favor the new building project is 0.096 or 9.6%.

User Bugs Bunny
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