Sociologists say that 95% of married women claim that their husband's mother is the biggest bone of contention in their marriages. Suppose that six married women are having coffee together. What's the probability all of them dislike their mother-in-law?

Oct 23, 2017

The probability that all 6 women dislike their mothers-in-law is 73.5%.

Explanation:

The probability that one of woman disliking her mother-in-law is:

${p}_{1} = 0.95$

The probability that two women dislike their mothers-in-law is (probability rules):

${p}_{2} = {p}_{1} \cdot {p}_{1} = {p}_{1}^{2} = {0.95}^{2} = 0.9025$

By extension it is simple to see that the case of all 6 disliking their mothers-in-law would be

${p}_{6} = {p}_{1}^{6} = {0.95}^{6} \cong 0.735$

Therefore the probability that all 6 women dislike their mothers-in-law is 73.5%.