Binomial where N value is too big

Question

It is estimated that 20% of students take an active part in a sports club in college. If 20 students are randomly sampled and asked if they are active participants in a college sports club what is the probability that more than 4 are active in a sports club?

So I am setting this up as a binomial and finding '1 - (p(0)+p(1)+p(2)+p(3)+p(4))'

However the N value is 20. Is there a simpler way of determining this?

but for example 20!/3!(17!) = 1.14x10^33 ...how do I get around these massive numbers? — Phillip Smith, May 26 '16 at 20:04
If you calculate this with a calculator do not forget to put braces around (3!*17!).
notice that 20! = 201918....1, and 17! = 1716...1. So dividing them gives: 20!/(17!3!) = (201918)/(321) = 10196. — Nescrio, May 26 '16 at 20:09

score 4 · Accepted Answer · answered May 26 '16 at 20:00

4

I'm not sure why N=20 is bothering you.
Hopefully you got these:
$P(0)=\begin{pmatrix}20\\0\end{pmatrix}0.2^00.8^{20}$
$P(1)=\begin{pmatrix}20\\1\end{pmatrix}0.2^10.8^{19}$
$P(2)=\begin{pmatrix}20\\2\end{pmatrix}0.2^20.8^{18}$
......

You'll have to use calculator anyway.

answered May 26 '16 at 20:00

Elissa

238

I was incorrectly using my calculator. Thanks – Phillip Smith May 26 '16 at 20:18

Binomial where N value is too big

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