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find the probability of exactly one successes in five trials of a binomial experiment in which the probability of success is 5%

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Answer:

Explanation:

To find the probability of exactly one success in five trials of a binomial experiment with a probability of success of 5%, we can use the formula for the probability mass function of the binomial distribution, which is:

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

where:

P(X = k) is the probability of k successes

n is the number of trials

k is the number of successes

p is the probability of success in one trial

(n choose k) is the binomial coefficient, which is the number of ways to choose k successes out of n trials

In this case, we want to find the probability of exactly one success, so k = 1, n = 5, and p = 0.05. Plugging these values into the formula, we get:

P(X = 1) = (5 choose 1) * 0.05^1 * (1-0.05)^(5-1)

= 5 * 0.05 * 0.95^4

≈ 0.2262

Therefore, the probability of exactly one success in five trials of a binomial experiment with a probability of success of 5% is approximately 0.2262, or about 22.62%.

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