The answer depends on whether you would accept an approximation and how accurate you want the approximation to be e.g. my answer to all problems is 1 [img]/images/graemlins/wink.gif[/img]
The most obvious "forward" way as you call it would be:
13/52 + (39/52)*(13/51)
It is always possible to factor out the 13/52 in this type of problem i.e.
<font class="small">Code:</font><hr /><pre>x/y + ((y - x)/y)*(x/(y - 1)) = x/y + (y - x)*x/((y - 1)*y)
= x/y + ((y - x)/(y - 1))*(x/y)
= (x/y)*(1 + (y - x)/(y - 1))</pre><hr />
This would look like:
(13/52)*(1 + 39/51)
in the problem at hand. It is about as economical to calculate as the "reverse" way, but has drifted away from how most people think.