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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the probability that exactly five out of ten voters will vote in favor of the initiative, we need to use the binomial probability formula:

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

Where:
- n = number of trials (10 voters)
- k = number of successes (5 voters)
- p = probability of success (0.76)
- (n choose k) is calculated as n! / (k! * (n-k)!)

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) = 0.16

Therefore, the probability that exactly five out of ten voters will vote in favor of the initiative is 0.16 or 16%.