IF L is length of burst error & polynomial generator has highest degree as r.
1.All burst errors with L ≤ r will be detected.
2.All burst errors with L = r + 1 will be detected with probability 1 – (1/2)r–1.
3.All burst errors with L > r + 1 will be detected with probability 1 – (1/2)r.
Now , as r = 8 here so it will be able to detect burst error of size 6 and it will dtect single bit error so option a and b are true
Now probabiltiy of detecting burst error of size 9 = 1-(1/2)^8 -------[by second rule as L = r+1, L=9 and r = 8]
and probabiltiy of detecting burst error of size 15 = 1-(1/2)^15-----[by third rule as L>r+1, L=15 and r = 8]
so both option c and option d are false