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 5.1% 5.1% 27.4% 27.4% 15% 15% 10%

Answer 1

[AI-generated answer — Bot GPT 3.5]

The probability of selecting exactly 5 voters in favor of the initiative out of 10 voters can be calculated using the binomial probability formula:

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

where:
n = total number of trials (10 voters)
k = number of successful outcomes (5 voters in favor)
p = probability of success (0.76)

Plugging in the values:

P(X = 5) = (10 choose 5) * (0.76)^5 * (1-0.76)^(10-5)

Calculating:

P(X = 5) = (252) * (0.76)^5 * (0.24)^5
P(X = 5) = 0.274

Therefore, the probability that exactly five of the ten voters selected will vote in favor of the initiative is 27.4%.