A poll shows that 76% of voters favor an initiative. If 7 voters are selected at random, what is the probability that exactly 4 of them will vote in favor?(1 point)
To calculate the probability that exactly 4 out of 7 voters will vote in favor, we can use the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
n = 7 (total number of voters)
k = 4 (number of voters in favor)
p = 0.76 (probability of a voter favoring the initiative)
Plugging in the values:
P(X = 4) = (7 choose 4) * 0.76^4 * (1-0.76)^(7-4)
P(X = 4) = (7! / (4! * (7-4)!)) * 0.76^4 * 0.24^3
P(X = 4) = (35) * 0.356449536 * 0.013824
P(X = 4) = 0.1761
Therefore, the probability that exactly 4 out of 7 voters will vote in favor is approximately 0.1761 or 17.61%.