A will send after $\{ 0,1,2,3\}$
Similarly B will send after $\{ 0,1,2,3......15\}$
Total Pairs = $4 \times 16=64$
B wins the backoff for these pairs $(A,B)= \{ (1,0),(2,0),(3,0),(2,1),(3,1),(3,2)\}$
Tie pairs where noone can send $\{ (0,0),(1,1),(2,2),(3,3\}$
Proability of 'A' winning = $1-\Large{ \frac{6}{64}- \frac{4}{64}} $ $= \Large \frac{54}{64} = 84.375 \%$