SOLUTION: Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of

Question 1178696: Assume that male and female births are equally likely and that the birth of any
child does not affect the probability of the gender of any other children. Find the probability of at most five girls in ten births.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Assume that male and female births are equally likely and that the birth of any
child does not affect the probability of the gender of any other children.
Find the probability of at most five girls in ten births.
~~~~~~~~~~~~~~~

It is a binomial distribution probability problem. - number of trials n = 10; - number of success trials k <= 5; - Probability of success on a single trial p = 0.5. We need calculate P(n=10; k<=5; 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=10; k<=5; p=0.5) = 0.623046875, or 0.6230 (rounded). ANSWER

Solved.

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To see a variety of 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).

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The number of girls in 10 births is either less than 5, or equal to 5, or more than 5:

P(less than 5 girls)+P(5 girls)+P(more than 5 girls) = 1

Because the probabilities for male or female are the same,

P(less than 5 girls) = P(more than 5 girls)

So

2*P(less than 5 girls) = 1-P(5 girls)
P(less than 5 girls) = (1-P(5 girls))/2

P(5) = C(10,5)*(0.5)^10 = 0.246 (to 3 decimal places)

P(less than 5 girls) = (1-0.246)/2 = 0.377

P(at most 5 girls) = P(less than 5 girls)+P(5 girls) = 0.377+0.246 = 0.623

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