Lesson Solving problems on Binomial distribution with Technology (using online solver)

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<H2>Solving problems on Binomial distribution with Technology (using online solver)</H2>

<H3>Problem 1</H3>Sociologists say that &nbsp;90% &nbsp;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 one morning.  &nbsp;What is the probability that:
<pre>

a) all of them dislike their mother-in law?

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?  
</pre>

<B>Solution</B>

<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.

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

- number of trials        n = 6;
         - number of success trial k = 6;
         - Probability of success on a single trial p = 0.9.

P(n=6; k=6; p=0.9) = 0.531441.      <U>ANSWER</U>

b)  none of them dislike their mother-in law?

- number of trials        n = 6;
         - number of success trial k = 0;
         - Probability of success on a single trial p = 0.9.

P(n=6; k=0; p=0.9) = 0.000001.     <U>ANSWER</U>

c)  at least four of them dislike their mother-in law?

- number of trials        n = 6;
         - number of success trial k >= 4;
         - Probability of success on a single trial p = 0.9.

P(n=6; k>=4; p=0.9) = 0.98415.     <U>ANSWER</U>

d) no more than three of them dislike their mother-in law?

- number of trials        n = 6;
         - number of success trial k <= 3;
         - Probability of success on a single trial p = 0.9.

P(n=6; k<=3; p=0.9) = 0.01585.     <U>ANSWER</U>
</pre>

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