Question 236924
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The probability of exactly *[tex \Large k] successes out of *[tex \Large n] trials is given by:


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


Where *[tex \Large p] is the probability of success on a given trial and *[tex \Large q] is the probability of failure and *[tex \Large \left(n\cr k\right)\ =\  \frac{n!}{k!(n-k)!}]


For your problem:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P_9(7)\ =\ \left(9\cr 7\right)(0.8)^7(0.2)^2]


You can do your own arithmetic.


Note that this is the probability that it will rain EXACTLY 7 of the next 9 days.  Questions about the probability that it will rain no more than 7 days or at least 7 days are very different questions. 



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