Question 1176021: The Smith family was one of the first to come to the U.S. They had 9 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had:
at least 6 girls?
at most 4 girls?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
The Smith family was one of the first to come to the U.S. They had 9 children.
Assuming that the probability of a child being a girl is 0.5, find the probability that the Smith family had:
(a) at least 6 girls?
(b) at most 4 girls?
~~~~~~~~~~~~~
(a) At least 6 girls means 6, 7, 8 or 9 girls, in this case.
It is a binomial distribution probability problem.
- number of trials n = 9;
- number of success trial k >= 6;
- Probability of success on a single trial p = 0.5.
We need calculate P(n=9; k>=6; p=0.5).
To facilitate calculations, I use an appropriate online (free of charge) calculator at this web-site
https://stattrek.com/online-calculator/binomial.aspx
It provides nice instructions and a convenient input and output for all relevant options/cases.
P(n=9; k>=6; p=0.5) = 0.25390625, or 0.2539 (rounded). ANSWER
(b) at most 4 girls means 0, 1, 2, 3, or 4 girls, in this case.
It is a binomial distribution probability problem.
- number of trials n = 9;
- number of success trial k <= 4;
- Probability of success on a single trial p = 0.5.
We need calculate P(n=9; k<=4; p=0.5).
Use the same online calculator at this web-site
https://stattrek.com/online-calculator/binomial.aspx
It gives P(n=9; k<=4; p=0.5) = 0.5. ANSWER
Solved.
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To see a variety similar solved problems, look into the lessons
- Simple and simplest probability problems on Binomial distribution
- Typical binomial distribution probability problems
- How to calculate Binomial probabilities with Technology (using MS Excel)
- Solving problems on Binomial distribution with Technology (using MS Excel)
- Solving problems on Binomial distribution with Technology (using online solver)
in this site.
After reading these lessons, you will be able to solve such problems on your own,
which is your PRIMARY MAJOR GOAL visiting this forum (I believe).
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