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?
5.1%
10%
27%
15%
10%
To calculate this probability, 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
k = number of successful trials (favoring the initiative) = 5
p = probability of success in a single trial = 0.76
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) = 0.0999 (approximately 10%)
Therefore, the probability that exactly five of the 10 voters will vote in favor of the initiative is 10%.