Question

Exercise 5-69 Algo

Assume that X is a hypergeometric random variable with N = 19, S = 7, and n = 6. Calculate the following probabilities. (Round your answers to 4 decimal places.)

a. P(X=1)

b. P(X=6)

C. P(X>or equal to 2)

Answer 1

P(X = x) = ₇C_x * ₁₂C_6-x / ₁₉C₆

a) P(X = 1) = 7C1 * 12C5 / 19C6 = 0.2043

b) P(X = 6) = 7C6 * 12C0 / 19C6 = 0.0003

c) P(X > 2) = 1 - [P(X = 0) + P(X = 1)]

                  = 1 - [(7C0 * 12C6 / 19C6) + 7C1 * 12C5 / 19C6]

                  = 1 - 0.2384

                  = 0.7616