Dane and Dana are playing a game on an m × n board. Dane places a rook on the bottom-left square, and then each takes a turn, with Dane going first, moving the rook either up any amount of squares or to the right any amount of squares. The person who does not have a move loses. If you randomly selects two integers m and n from the set {1, . . . , 10} (with replacement) to be the dimensions of the board and both players play rationally, the probability that Dane wins the game can be expressed as a b , where (a, b) = 1. Find a + b.