Question

uppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x.

Answer 1

Hypergeometric probabilities are calculated using combinations that represent the number of ways to choose x successes out of r possible, and n - x failures out of N - r possible, divided by the total number of ways to choose n items out of N.

Step-by-step explanation:

The question pertains to the computation of hypergeometric probabilities for a given N, r, and various values of n and x. In hypergeometric distribution, the variables r, b, and n represent the size of the group of interest, the size of the second group, and the size of the chosen sample, respectively. To find the hypergeometric probability P(X = x) for specific values of n and x, you would use the formula:

`P(X = x) = [(C(r, x) * C(N- r, n - x)) / C(N, n)]`

where C(a, b) is the combination of a objects taken b at a time. For example, if you wanted to know the probability of drawing exactly 2 men (x = 2) from a group of 6 men (r = 6) and 5 women (b = 5) in a committee of 4 people (n = 4), you would substitute these values into the formula and perform the calculations using combinations.