Question

Sociologists say that 90% 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. (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.

Please provide formulas!

Answer 1

n = 8

p = 0.9

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

a) P(X = 8) = 8C8 * (0.9)^8 * (0.1)^0 = 0.430

b) P(X = 0) = 8C0 * (0.9)^0 * (0.1)^8 = 0.000

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

                 = 8C6 * (0.9)^6 * (0.1)^2 + 8C7 * (0.9)^7 * (0.1)^1 + 8C8 * (0.9)^8 * (0.1)^0

                  = 0.962

d) P(X < 5) = 1 - P(X > 5)

                = 1 - ( P(X = 6) + P(X = 7) + P(X = 8))

                = 1 - (8C6 * (0.9)^6 * (0.1)^2 + 8C7 * (0.9)^7 * (0.1)^1 + 8C8 * (0.9)^8 * (0.1)^0)

                = 1 - 0.962

               = 0.038