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% 5.1% 5.1% 27.4% 27.4% 15% 15%
27.4%
To calculate the probability of exactly five out of ten voters favoring the initiative, we can use 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 trials (5 voters)
- p = probability of success on a single trial (0.76 in this case)
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) = 27.4%
Therefore, the probability of exactly five out of ten voters favoring the initiative is 27.4%.