Question 1033050
<font face="Times New Roman" size="+2">


The probability of *[tex \Large k] successes in *[tex \Large n] trials where *[tex \Large p] is the probability of success on any given trial is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P_n(k,p)\ =\ {{n}\choose{k}}\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k}]


Where *[tex \LARGE {{n}\choose{k}}] is the number of combinations of *[tex \Large n] things taken *[tex \Large k] at a time and is calculated by *[tex \Large \frac{n!}{k!(n\,-\,k)!}]


You need to calculate the probability of 0 correct plus the probability of 1 correct plus the probability of 2 correct plus the probability of 3 correct plus the probability of 4 correct plus the probability of 5 correct.  Symbolically:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P_7(\leq\,5,0.20)\ =\ \sum_{k\,=\,0}^5\,{{7}\choose{k}}\left(0.2\right)^k\left(0.8\right)^{7\,-\,k}]


Which is 6 probability calculations and 6 sums.  Easier would be:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P_7(\leq\,5,0.20)\ =\ 1\ -\ \sum_{k\,=\,6}^7\,{{7}\choose{k}}\left(0.2\right)^k\left(0.8\right)^{7\,-\,k}]


calculating the probability of 6 correct plus the probability of 7 correct and then subtracting from 1.  2 probability calculations and 3 sums.


Easier yet, if you have access to Microsoft Excel on a PC or Numbers on a Mac, open a spreadsheet, pick a cell, and type:


<pre>
=BINOMDIST(5,7,.02,TRUE)
</pre>

When you hit enter, you get your answer.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>