Question 386535: If 20 people where selected at random, what is the probability that exactly 12 of those people have brown eyes?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
That depends. What is the probability that any one person selected at random has brown eyes? You would have to define the target population first as I'm sure P(brown) is different in the Northern Europe universe vs. the South America universe, for example. Be that as it may, let us assume that there is a number  that represents the probability that any one person has brown eyes according to the population constraints that you establish. Note that  .
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 !})
For your problem,  ,  , and, for the time being, will just be left as a placeholder.
\ =\ \left(20\cr 12\right\)p^{12}\left(1\,-\,p\right)^{8})
Once you have determined the appropriate value of , fill it in and do the indicated arithmetic. If you are required to show your arithmetic work, you have quite a task ahead of you -- better start now. On the other hand, if you just need the answer and you have MS Excel or Apple Numbers available to you, open a blank spread sheet, select any cell you like, and type the following AFTER you have a valid value for .
)
Hit Enter and you will have your answer.
John
My calculator said it, I believe it, that settles it
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