Question

what exactly the probability fir detecting Burst errors?

Answer 1

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.

example - For x⁶ + 1        

This generator can detect all burst errors with a length less than or equal to 6 bits; 3 out of 100 burst errors with length 7 will slip by; 16 out of 1000 burst errors of length 8 or more will slip by.

Source - Behrouz A. Forouzan

Comments

Adding some more points:

if polynomial contains a factor of (x + 1), then  It can detect the odd number of bit errors.

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@saurav raghaw it detect all odd number of error if x+1 is factor of generator polynomial