Question

A poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. If 10 voters are selected at random, what is the probability that exactly five of them will vote in favor of the initiative?(1 point) Responses 10% 10% 27.4% 27.4% 15% 15% 5.1%

Answers

GPT 3.5
27.4%

To find the probability of exactly five out of ten voters in favor of the initiative, we can use the binomial probability formula:

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

where n is the number of trials (10 voters selected), k is the number of successful outcomes (5 voters in favor), p is the probability of success on each trial (76% or 0.76).

Plugging in the values:
P(X = 5) = (10 choose 5) * (0.76)^5 * (1-0.76)^(10-5)
P(X = 5) = 252 * 0.76^5 * 0.24^5
P(X = 5) ≈ 0.2744

Therefore, the probability of exactly five voters out of ten voting in favor of the initiative is approximately 27.4%.

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