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