All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
proposed solution | Comment 1 of 4
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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information