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Two distinct integers, x and y, are randomly chosen from the set {1,2,3,4,5,6,7,8,9,10}. What is the probability that xy-x-y is even?

 Aug 23, 2019
 #1
avatar+102913 
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 If x is odd and y is odd then

 

(odd) (odd)  - (odd) - (odd)   = 

     odd  -  odd - odd   =

             even - odd =

                  odd

 

If x is odd and y is even then

(odd)(even) - odd -even =

    even  - odd - even  =

         odd - even  =

               odd

 

So...    xy - x - y     will only be even when  x,y are even

 

We have  these possible even pairs

2,4         4,6        6, 8     8,10    

2,6         4,8        6.10

2,8         4,10      

2,10 

 

So 10 pairs  produce an even result  for   xy - x-  y 

 

And the number of possible pairs is  C(10,2)  =  45

 

So....the probability that  xy - x - y   is even  =   10  / 45   =  2 / 9

 

cool cool cool

 Aug 24, 2019

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