Question

Sociologists say that 80% of married women claim that their husband's mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that eight married women are having coffee together one morning. Find the following probabilities. (For each answer, enter a number. Round your answers to three decimal places.) (a) All of them dislike their mother-in-law. (b) None of them dislike their mother-in-law. (c) At least six of them dislike their mother-in-law. (d) No more than five of them dislike their mother-in-law.

Answer 1

p = 0.8

n = 8

P(X = x) = 8Cx * 0.8^x * (1 - 0.8)^8-x

a) P(X = 8) = 8C8 * 0.8⁸ * 0.2⁰ = 0.168

b) P(X = 0) = 8C0 * 0.8⁰ * 0.2⁸ = 0

c) P(X > 6) = P(X = 6) + P(X = 7) + P(X = 8)

                   = 8C6 * 0.8⁶ * 0.2² + 8C7 * 0.8⁷ * 0.2¹ + 8C8 * 0.8⁸ * 0.2⁰

                   = 0.797

d) P(X < 5) = 1 - P(X > 6) = 1 - 0.797 = 0.203