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?

27.4%

10%

15%

5.1%

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the probability that exactly five out of ten voters will vote in favor, we need to 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 in favor)
p = probability of success on each 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) = 252 * 0.10301 * 0.002915
P(X=5) = 0.0751

So, the probability that exactly five out of ten voters will vote in favor of the initiative is approximately 7.51%, which is closest to option 5.1%.