SOLUTION: Two digits are randomly selected without repetition, compute probability tha their sm is odd... also that their product is odd

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Question 475455: Two digits are randomly selected without repetition, compute probability tha their sm is odd... also that their product is odd
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
For the sum being ODD is solved here:
http://www.algebra.com/cgi-bin/jump-to-question.mpl?question=475441
For the product being ODD 

EVEN × EVEN = EVEN
EVEN × ODD = EVEN
ODD × EVEN = EVEN
ODD × ODD = ODD

So to have their product odd, they have to both be odd.

The digits are

0,1,2,3,4,5,6,7,8,9

5 are ODD and 5 are EVEN.

After we have chosen the first digit, there are only 9 digits 
left to choose from:

P[(odd 1st AND odd 2nd) =

AND indicates multiplication:

  P(odd 1st)×P(odd 2nd) =

       (5/10)(4/9) 

       (1/2)(4/9) 

          4/18

           2/9   
          
Edwin