Please Solve this Q

Question

Answer 1

for station A

n1 (number of collision of a) = 2,

Random number Range R2(0,2ⁿ -1) which is (0,1,2,3)

For Station B

n2 (number of collision of b) = 2

Random number Range R2(0,2ⁿ -1) which is (0,1,2.....15)

A will won the station when R1 < R2 which is (14+13+12+11)  =50 times  

Probability of winning of A = 50/60

Answer 2

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}} $ $=  \Large \frac{54}{64} = 84.375 \%$