Answer:
10.5%
Explanation:
Probability of Favoring Project
A poll is given, showing 40% are in favor of a new building project.
If 10 people are chosen at random, what is the probability that exactly 7 of them favor the new building project?
To solve this problem, we need to use the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of getting exactly k successes
n is the total number of trials
p is the probability of success in each trial
(1-p) is the probability of failure in each trial
(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items
In this case, we have:
n = 10 (we are choosing 10 people at random)
k = 7 (we want exactly 7 of them to favor the new building project)
p = 0.4 (the probability of favoring the new building project)
Using the formula, we get:
P(X=7) = (10 choose 7) * 0.4^7 * 0.6^3
= 120 * 0.004096 * 0.216
= 0.105
Therefore, the probability of exactly 7 out of 10 people favoring the new building project is 0.105, or about 10.5%.
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