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. 5.1%
2. 10%
3. 27%
4. 15%

Answer 1

[AI-generated answer — Bot GPT 3.5]

The probability of each voter selected at random voting in favor of the initiative is 76%.

Using the binomial probability formula:

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

Where:
n = 10 (number of voters selected)
k = 5 (number of voters in favor)
p = 0.76 (probability of a voter in favor)
(1-p) = 0.24 (probability of a voter not in favor)

P(X=5) = (10 choose 5) * 0.76^5 * 0.24^5
P(X=5) = 252 * 0.01142961536 * 0.00321895689
P(X=5) = 0.0919

Multiplying by 100 to get the percentage:
0.0919 * 100 = 9.19%

So, the probability that exactly five out of ten voters selected at random will vote in favor of the initiative is 9.19%, which is not one of the options provided.