What Nauseated and I both forgot is that bishops can only ever be on one colour.
This will not change the answer but I will still make the working more accurate.
So there is not 64 squares that they can be on there is only 32 possible squares!
I wasn't about to just take your word for it so I also worked it out.
I got exactly the same answer but my working was a little different.
I said that for 14 out of 32 squares the bishop would be a threat to 7 out of 63 squares
then I said that for 10 out of 32 squares the bishop would be a threat to 9 out of 63 squares
then I said that for 6 out of 32 squares the bishop would be a threat to 11 out of 63 squares
then I said that for 2 out of 32 squares the bishop would be a threat to 13 out of 63 squares
So the probability that the bishop would be a threat to the rook is
$$\\\mbox{P(they are a threat to each other)}=0\\\\
\mbox{P(the rook is a threat to the bishop)}=\frac{2}{9}\\\\
\mbox{P(the bishop is a threat to the rook)}\\\\
=\frac{14}{32}\times\frac{7}{63}+\frac{10}{32}\times\frac{9}{63}+\frac{6}{32}\times\frac{11}{63}+\frac{2}{32}\times\frac{13}{63}\\\\
=\frac{(14*7)+(10*9)+(6*11)+(2*13)}{32*63}\\\\
=\frac{280}{2016}\\\\
=\frac{5}{36}\\\\
so\\
\mbox{P(that any threat is presented)}=\frac{2}{9}+\frac{5}{36}-0=\frac{13}{36}$$
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