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%.
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
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