Question 1038464
<font face="Times New Roman" size="+2">


You want the probability that the machine will be working, so you want the probability of 2 or fewer occurrences of a failure in 15 trials given the probability of success on any given trial is 0.08.


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)!}]


Since you are looking for the probability of 2 or fewer, you need the probability of 0 plus the probability of 1 plus the probability of 2, that is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P_{15}(\leq{2},0.08)\ =\ \sum_{k\,=\,0}^{2}\,{{15}\choose{k}}\left(0.08\right)^k\left(0.92\right)^{15\,-\,k}]


An easier way to get the answer, given that you have MS Excel on your PC or Numbers on your MAC, is to open a spreadsheet and type the following:
<pre>
       =BINOMDIST(2,15,0.08,TRUE)
</pre>


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>