Question

Sociologists say that 95% 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 nine 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 seven of them dislike their mother-in-law.

(d) No more than six of them dislike their mother-in-law.

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

P(dislike mother-in-law), p = 0.95

q = 1 - p = 0.05

n = 9

a) P(all of them dislike their mother-in-law) = 0.95⁹

= 0.6302

b) P(none of them dislike their mother-in-law) = 0.05⁹

= 1.953x10^-12

c) P(at least seven of them dislike their mother-in-law) = P(7) + P(8) + P(9)

= 9C7x0.95⁷x0.05² + 9x0.95⁸x0.05 + 0.95⁹

= 0.9916

d) P(no more than six of them dislike their mother-in-law) = 1 - P(at least seven of them dislike their mother-in-law)

= 1 - 0.9916

= 0.0084