Question

Let N = 8, r = 3, and n = 4. Using the hypergeometric probability distribution, find P(X ≤ 1) =

Answer 1

To find P(X ≤ 1) using the hypergeometric probability distribution, we need to calculate P(X = 0) + P(X = 1). Using the formula for the hypergeometric distribution, we can find P(X = k) = (rCk)*(bC(n-k))/(r+bCn).

Step-by-step explanation:

P(X ≤ 1) is the probability that the number of men on the committee is less than or equal to 1. Using the hypergeometric probability distribution, we can calculate this probability. In this case, r = 6 (number of men), b = 5 (number of women), and n = 4 (committee size).

To find P(X ≤ 1), we need to calculate P(X = 0) + P(X = 1). Using the formula for the hypergeometric distribution, we can find P(X = k) = (rCk)*(bC(n-k))/(r+bCn), where nCk represents the combination (n choose k).

Calculating P(X = 0): P(X = 0) = (6C0)*(5C4)/(11C4) = 5/330 = 0.0152

Calculating P(X = 1): P(X = 1) = (6C1)*(5C3)/(11C4) = 30/330 = 0.0909

Therefore, P(X ≤ 1) = P(X = 0) + P(X = 1) = 0.0152 + 0.0909 = 0.1061