Question 1087657
A = { A, J, or 7 drawn }
B = { all the other cards }

So yes, there are 12 cards of interest.   That means there are 40 other cards. 

Pr(A) = 1 - Pr(only cards from B are drawn)
          = 1 - (40/52)*(39/51)*(38/50)
           = 1 - (38/(17*5))  
           ~= {{{ highlight(0.55294) }}}

( ~= used to indicate approximation)