A committee of 5 people is to be formed from 11 civil employees and 8 small business people. what is the probability that none of the people selected are small business people? using hypergeometric distribution
To calculate the probability that none of the people selected are small business people, we can use the hypergeometric distribution formula:
P(X = k) = (C(k, k) * C(N - n, n - k)) / C(N, n)
Where:
- N is the total population (11 civil employees + 8 small business people = 19)
- n is the total number of successes in the population (8 small business people)
- k is the number of successes in the sample (0 small business people)
Plugging in the values:
P(X = 0) = (C(0, 0) * C(11, 5)) / C(19, 5)
Calculating the combinations:
C(0, 0) = 1
C(11, 5) = 462
C(19, 5) = 11628
Plugging in the values:
P(X = 0) = (1 * 462) / 11628
P(X = 0) = 462 / 11628
P(X = 0) = 0.0397
Therefore, the probability that none of the people selected are small business people is 0.0397, or 3.97%.