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The middle number (Posted on 2019-10-08) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (1 votes)

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proposed solution | Comment 1 of 5
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 2019-10-08 13:09:29
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