Question 1001783
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This is a binomial distribution where you want the probability of 30 successes in 30 trials where the probability of success on any given trial is 0.20 (one in five).


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


Plugging in your numbers:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P_{30}(30,0.2)\ =\ {{30}\choose{30}}\left(0.2\right)^{30}\left(0.8\right)^{0}\ =\ 0.2^{30}\ \approx\  0.000000000000000000001074]


Expressing it in terms of odds, that is roughly 999,999,999,999,999,999,999 to 1 against.  A DNA match isn't that conclusive.  Somebody peeked.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

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