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?
Before worrying about the middle number, consider the other four.
The two smallest numbers must each be < .6 with probability 3/5.
Likewise, the two largest must each be > .4 with probability 3/5.
Then the middle is > .4 and < .6 with probability 2/5.
Those events are independent so the probability is (2/5)*(3/5)^4
= 162/3125 = 0.05184, a bit more than 1/20.
Offhand that seems low.

Posted by xdog
on 20191008 13:09:29 