Given 5 numbers, each randomly chosen between zero and one, what is the probability that the number in the "middle" (the third one when sorted) is between 0.4 and 0.6?

The sum of all probabilities equals 1.  So determine NOT probability.  Middle number will not be in range if 3 or more numbers are above 0.6 or below 0.4.

Prob. of 3 = 0.4 * 0.4 * 0.4 * 0.6 * 0.6 = 0.02304
Prob. of 4 = 0.4 * 0.4 * 0.4 * 0.6 * 0.6 = 0.01536
Prob. of 5 = 0.4 * 0.4 * 0.4 * 0.6 * 0.6 = 0.01024

Sum = 0.04864
Sum * 2 (< 0.4 or > 0.6) = 0.09728

Thus, the probability of the middle number being between 0.4 and 0.6 is xxxxxx

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Edit:  After plugging 5^5 combinations into excel, I agree with Bryan Smith's answer.  Not sure where I went wrong with the math, but Probability was never my strong suit.

36.512 %

Edited on January 14, 2020, 9:29 pm

Posted by hoodat on 2020-01-14 16:58:20