Question 1198224
.
Sociologists say that 80% of married women claim that their husband’s mother 
is the biggest bone of contention in their marriages. 
Suppose that 5 married women are having coffe together one morning. 
What is the probability that :
(1) exactly 3 of then dislike their mother- in law ?
(2) all of them dislike their mother- in law ?
(3) none of them dislike their mother -in law?
(4) at least 4 of them dislike their mother in law?
(5) no more than 3 of them dislike their mother in law ?
(7) what is the expected number of women who dislike their mother in law ? 
    What is the standard deviation of the distribution?
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<pre>
It is a binomial distribution probability problem.


To facilitate my calculations, I will use an appropriate online (free of charge) calculator 
at this web-site 

https://stattrek.com/online-calculator/binomial.aspx


It provides a convenient input (and output) for all relevant options/cases.


(1)  exactly 3 of them dislike their mother-in-law ?

         - number of trials        n = 5;
         - number of success trial k = 3;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k=3; p=0.8) = 0.2048  (rounded).      <U>ANSWER</U>


(2)  all of them dislike their mother-in law?

         - number of trials        n = 5;
         - number of success trial k = 5;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k=5; p=0.8) = 0.3277  (rounded).     <U>ANSWER</U>


(3)  none of them dislike their mother-in-law?

         - number of trials        n = 5;
         - number of success trial k = 0;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k=0; p=0.8) = 0.00032.     <U>ANSWER</U>


(4)  at least 4 of them dislike their mother-in-law?

         - number of trials        n = 5;
         - number of success trial k >= 4;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k>=4; p=0.8) = 0.7373  (rounded).    <U>ANSWER</U>


(5) no more than 3 of them dislike their mother-in-law?

         - number of trials        n = 5;
         - number of success trial k <= 3;
         - Probability of success on a single trial p = 0.8.

           P(n=5; k<=3; p=0.8) = 0.2627  (rounded).     <U>ANSWER</U>


(7)  The expected number of this binomial distribution is n*p = 5*0.8 = 4.

     The standard deviation is  s = {{{sqrt(p*n*(1-p))}}} = {{{sqrt(0.8*5*(1-0.8))}}} = 0.8944  (rounded).
</pre>

Solved.


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Do not think that this problem is very original. Similar problems come often to this forum.


See, for example, this link


https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1160081.html


(it came couple of years ago . . . )