Consider a sender is trying to send three information bits a1, a2, and a3 over a noisy channel with error probability p = 0.001.

That is with probability p each bit may be flipped independently from 0 to 1 and vice versa.

The sender adds three parity bits to it as follows:

a4 = a2 + a3 (mod 2)

a5 = a1 + a3 (mod 2)

a6 = a1 + a2 (mod 2)

Compute the probability that the receiver makes an incorrect decision?

What happens if the sender only adds two parity bits a4 and a5?