+0  
 
+1
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avatar+108 

A checker is placed in a random square in the diagonal of an ordinary 8x8 checkerboard (with all squares being equally likely).

Checkers are then placed in the squares that lie below and to the right of the first checker, including those squares that are directly below or directly to the right of the first checker.

What, then, is the expected number of checkers on the board?

 

Can I have a hint, or the solution?

Max0815  Jul 25, 2018
 #1
avatar+4 
0

Could you start with the amount of options there are for a square to be chosen?  Would that matter?

KaBoom  Jul 25, 2018
 #2
avatar+108 
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there are 8 choices for the first checker...idk if it matters

Max0815  Jul 26, 2018
 #3
avatar+87537 
+1

Here's my best effort....

 

Since a checker is placed on a diagonal....we have 8  possibilities  for the checker's placement

 

If we place the checker on Row 1, Column 1   we have  64 total checkers  = 8^2

If we pllace the checker on Row2, Column 2, we have 49 total checkers  = 7^2

Following this pattern, the expected value is

 

[8^2 + 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1^2 ] / 8  =   204 / 8 =  51/2 =  25.5 checkers

 

 

cool cool cool

CPhill  Jul 26, 2018
 #4
avatar+108 
+1

thanks you, i was haveing a very hard time with this problem. Thanks cphill!!!

Max0815  Jul 26, 2018

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