Question 1124881
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The probability of *[tex \Large k] successful outcomes of *[tex \Large n] experiments where the probability of success on any given trial is *[tex \Large p] is given by:


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


The probability of <u>at least</u> *[tex \Large k] successful outcomes of *[tex \Large n] experiments where the probability of success on any given trial is *[tex \Large p] is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(\geq{k},n,p)\ =\  \sum_{r=k}^n\,{{n}\choose{r}}\(p\)^r\(1\,-\,p\)^{n\,-\,r}]


Although it may be more convenient to calculate the equivalent expression:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(\geq{k},n,p)\ =\  1\ -\ P(<k,n,p)\ =\ 1 - \sum_{r=0}^{k-1}\,{{n}\choose{r}}\(p\)^r\(1\,-\,p\)^{n\,-\,r}]


All you need to do is plug in your given numbers and do the arithmetic.  In the case of your specific problem, the "equivalent expression" will be much simpler to calculate for your second problem.  Don't forget that the probability must be expressed as a decimal.
								
								
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 \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}
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