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avatar+662 

Suppose we have a bag with $10$ slips of paper in it.  Eight slips have a $3$ on them and the other two have an $8$ on them. 

 

How many $8$'s do we have to add to make the expected value equal to $4$?

 Dec 21, 2023
 #1
avatar+126978 
+1

Let the number of "8" slips we need to  add = N

 

So

 

3 ( 8 / (10 + N) )   +   8 ( 2+ N) / (10 + N )  =  4       simplify

 

[ 24 + 16 + 8N ]  / (10 + N)  = 4

 

[ 40 + 8N ] =  4 (10 + N)

 

40 + 8N  =  40 + 4N

 

8N = 4N

 

(8- 4) N = 0

 

4N  = 0

 

N =  0         (we don't need to  add any !!! )

 

 

Proof   :   

 

Expected value =  Outcome * Probability  =   3 (8/10)  + 8(2/10)  =  [ 24 + 16 ] / 10  =  40 / 10    = 4

 

 

cool cool cool

 Dec 21, 2023

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