Question

for the binary symmetric channel with input X,output Y and alphabet {0,1}, the probability of a channel error is P(Y=0/X=1)=p(Y=1/X=0)= 0.1. In order to improve transmission accuracy each bit is repeated twice: 000 is sent for a 0 and 111 is sent for a 1. Find the probability of a symbol error when majority rule is used to determine whether a 1 or a 0 was transmitted.