Sociologists say that 85% of married women claim that their husband\'s mother is

Question

Sociologists say that 85% 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 six 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. Incorrect: Your answer is incorrect. (b) None of them dislike their mother-in-law. (c) At least four of them dislike their mother-in-law. (d) No more than three of them dislike their mother-in-law.

Explanation / Answer

X ~ Binomial( n, p )

Where n = 6 , p = 0.85

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

a)

P( X = 6) = 6C6 0.856 0.150

= 0.377

b)

P( X = 0) = 6C0 0.850 0.156

= 0.000

c)

P( X >= 4) = P( X = 4) + P( X = 5) + P( X = 6)

= 6C4 0.854 0.152 +6C5 0.855 0.15 +6C6 0.856 0.150

= 0.176

d)

P( X <= 3) = P( X = 0) + P( x =1) + P( X = 2) + P( X = 3)

= 6C0 0.850 0.156 +6C1 0.851 0.155 +6C2 0.852 0.154 +6C3 0.853 0.153

= 0.047

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