Statistics: Binomial Probability

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 twelve married women are having coffee together one morning. Find the following probabilities. (Round your answers to three decimal places.) find the probability that At least ten of them dislike their mother-in-law.

Answer 1

This problem can be solved using the binomial probability distribution, where:

1. n = 12 (number of trials, i.e., number of married women)
2. p = 0.95 (probability that a woman dislikes her mother-in-law)
3. x is the number of women who dislike their mother-in-law.

We're interested in finding the probability that at least 10 women dislike their mother-in-law. This is represented as:

P(X ≥ 10)

We can break it down using the binomial probability formula:

P(X ≥ 10) = P(X = 10) + P(X = 11) + P(X = 12)

The binomial probability formula has the following parameters:

1. The n and x in the parentheses with n on top is the number of combinations of choosing x objects from n.
2. p is the probability of success, and 1 − p is the probability of failure.

After plugging in the values for each P(X) and summing them up, the probability that at least ten of the twelve married women dislike their mother-in-law is 0.980 (rounded to three decimal places).

Hope this was helpful.