Question 1113205
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The probability of *[tex \Large k] successes in *[tex \Large n] trials with a probability of success on any single trial is *[tex \Large p] is given by:


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


You want to calculate


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P\(6,6,\frac{1}{38}\)\ =\ {{6}\choose{6}}\ \(\frac{1}{38}\)^6\,\cdot\,\(\frac{37}{38\)^{0}]


Note that *[tex \LARGE {{n}\choose{n}}=\ 1] for all positive integers *[tex \LARGE n] and *[tex \LARGE a^0\ =\ 1] for all real numbers *[tex \LARGE a].  Hence your calculation reduces to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P\(6,6,\frac{1}{38}\)\ =\ \(\frac{1}{38}\)^6]


Break out your calculator...


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">
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