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?
(In reply to proposed solution
The reason it seems low is that the median value is the one that's most likely to be in the given range. Since any given one of the five has 1/5 probability of being in the middle range, the probability should be greater than 1/5.
Remember that the first drawn is not destined to be the lowest, and likewise, the third drawn is not necessarily the middle one numerically (i.e., after sorting, that is the median).
Posted by Charlie
on 2019-10-08 13:35:47