If 90 % of married women claim that their husband's mother is the biggest bone of contention in...

Question:

If {eq}90 \ \% {/eq} of married women claim that their husband's mother is the biggest bone of contention in their marriages. Suppose that twelve married women are having coffee together one morning. Find the following probabilities.

(a) All of them dislike their mother-in-law

(b) None of them dislike their mother-in-law

(c) At least ten of them dislike their mother-in-law

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

Binomial Distribution

Binomial Distribution is the probabilities of repeated trials where each trial has one of two possible outcomes. The tossing of a coin with repetition is an example of a binomial situation.

Answer and Explanation:


a

The probability that all of them dislike their mother-in-law is {eq}\approx{0.28} {/eq}


Use the Excel formula "BINOM.DIST". The 4 inputs to the formula are: number of successes, number of trials, probability of success, and true for the cumulative probability and false for the probability of an exact number.


The result is:

{eq}\text{BINOM.DIST(12,12,0.9,FALSE)} \approx{0.28} {/eq}


b.

The probability that none of them dislike their mother in law is {eq}\approx {0} {/eq}

Substituting values:

{eq}\text{BINOM.DIST(0,12,0.9,FALSE)} = 1 * 10^{- 12} {/eq}


c.

The probability that at least ten of them dislike their mother-in-law is 0.89.


In This situation use the formula to get the probability of 9 or less and subtract if from 1 which will give the probbilut of at least 10.

Substituting values:

{eq}1 - \text{BINOM.DIST(9,12,0.9,TRUE)} \approx{0.89} {/eq}


d.

The probability that no more than tow of them dislike their mother-in-law is {eq}\approx{0} {/eq}

Substituting values, note: put True in the final input to get the probability of 2 or less.

{eq}\text{BINOM.DIST(2,12,0.9,TRUE)} \approx{5.5 * 10^{- 9}} {/eq}


Learn more about this topic:

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How to Use the Binomial Theorem to Expand a Binomial

from Algebra II Textbook

Chapter 21 / Lesson 16
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