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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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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). ANSWER
(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). ANSWER
(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. ANSWER
(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). ANSWER
(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). ANSWER
(7) The expected number of this binomial distribution is n*p = 5*0.8 = 4.
The standard deviation is s = = = 0.8944 (rounded).
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 . . . )