Question 271712
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The probability of exactly *[tex \Large k] successes in *[tex \Large n] trials where the probability of success on any given trial is *[tex \Large p] is given by:


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


Where *[tex \Large \left(n\cr k\right)] is the number of ways to select *[tex \Large k] things from a collection of *[tex \Large n] things and is equal to *[tex \Large \frac{n!}{k!\left(n\,-\,k\right)!}]


Since there are 5 responses to each question, the probability of a random correct response on any given question is *[tex \Large \frac{1}{5}\ =\ 0.2].


Just plug in the numbers...



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P_{60}\left(40\right)\ =\ \left(60\cr 40\right)\left(0.2\right)^{40}\left(0.8\right)^{20}]


And do the arithmetic.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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