SOLUTION: Me again. Hi - I know this is probably really simple, are I do not know if I am on the right track for this question (probability is just not making any sense to me at all).

Question 880388: Me again.
Hi - I know this is probably really simple, are I do not know if I am on the right track for this question (probability is just not making any sense to me at all).
It is known that 25% of all staff in a company make use of the free influenza vaccination programme. Answer the following as: The probability is equal to: (Round your probability to 4 decimal places:
Q If 20 people are randomly selected, find the probability that exactly 12 people don't use the vaccination programme.

Please help!
Thanks in advance!
Found 2 solutions by ewatrrr, KMST:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
p(make use of vaccine) = .25 n = 20
P(x=12) = 20C12(.25)^12(.75)^8 0r binompdf(20, .25, 12)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I think we are all reading it wrong.
THE ANSWER:
Maybe you just want the answer. In that case, I calculated the approximate probability that 12 of those 20 people got vaccinated as
, but I think you may really have meant what is the probability that of the were not vaccinated.
Then, it would be

THE CALCULATION:
Maybe you want to know how to calculate it.
If you have a computer with the right software, or a calculator with enough functions, you can calculate combinations of 20 taking 12 at a time as 20C12= .
With a simpler calculator, or (gasp!) with pencil and paper,
you would calculate it as
20C12=20C8= .
With most calculators or using your computer you can calculate (approximately) and
(approximately).
Then you calculate your approximate probability as
, which rounds to .
With pencil and paper it gets a little more cumbersome.

THE REASON WHY YOU APPLY "THE BINOMIAL DISTRIBUTION":
Maybe you want to understand why.
You can describe all the possible outcomes of randomly picking of the people in the staff of that company by the binomial
, meaning that
there is a probability that he/she got the vaccine and
there is a probability that he/she did not get the vaccine.
If you pick people, you can describe all the possible outcomes as the square of that binomial:
.
That means there is a probability that both goth the vaccine;
there is a probability that one or the other (got the vaccine(but not both),
and there is a probability that both are unvaccinated.
If you pick people, the whole spectrum of probabilities is described by the 20th power of that binomial:

In that long polynomial, the coefficient of the term with represents the probability that exactly of those people were vaccinated, and the other did not use he vaccination programme.
RELATED QUESTIONS
Hi - I know this is probably really simple, are I do not know if I am on the right track... (answered by ewatrrr,rothauserc)
Hi, I am not sure if I am figuring this out correctly and do not want to go any further... (answered by nerdybill)
Please Please Help Me!!! I am stuck on one question that I have probably trying to... (answered by edjones)
i am a homeschooled student i do not have text book curriculum. this question is probably (answered by stanbon)
Hi! I am trying to solve this question for my homework, but I am having trouble. The... (answered by Techpriest,MathTherapy)
Hello I'm really stuck on this question and would be very grateful if you could help... (answered by jim_thompson5910)
hi, my name is nia. i am having a problem with equations. i think it's called equation... (answered by Alan3354)
I would like to know if I am on the right track or not in answering this question. 5-5A... (answered by stanbon)