Question 333310: 1. Suppose a survey of 890 families with 5 children was done
a) What is the probability of observing children to be all boys or all girls
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
It depends. What are your assumptions regarding the probability of conception of a boy vs. a girl? If you presume 50/50, which is totally false, then you would proceed thus:
The probability of  successes in  trials where  is the probability of success on any given trial is given by:
\ =\ \left(n\cr k\right\)p^k\left(1\,-\,p\right)^{n\,-\,k})
Where ) is the number of combinations of things taken at a time and is calculated by !})
To calculate the probability of all boys in 5, you would use:
\ =\ \left(5\cr 5\right\)(0.5)^5(0.5)^0)
Fortunately, this reduces to a very simple calculation because \ =\ 1\ \forall\ n\ >\ 0\ \in\ \mathbb{Z}) . And  .
Since the probability is 1/2, the probability of 5 girls is the same, so the probability of either is just two times either.
If you want to assume the empirical probability of a boy being 105/205 or approximately 0.512, then you need to do:
\ +\ P_5(5,0.488)\ =\ (0.512)^5\ +\ (0.488)^5)
Once you decide on which probability to use, multiply by 890 to find the expected number.
John
My calculator said it, I believe it, that settles it
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