the solution currently provided on chegg is wrong. please can you provide a correct solution

(a) Consider the code C={0,1} as the input to a binary symmetric channel with bit-error probability 0.1. (i) What is the lowest achievable probability of mistake, if the receiver does not know the input probability distribution [p p0 1-p p0 ? Discuss. What detection rule should the receiver use? (ii) What is the lowest achievable probability of mistake, if the receiver knows that the probability distribution of the input is [0.99 0.01] ? Discuss. What detection rule should the receiver use