A communications channel transmits the dig$-$

its $0$ and $1.$ However, due to static, the digit

transmitted is incorrectly received with prob$-$

ability $0\mathrm{.}2.$ To reduce the chance of error, we

transmit $00000$ instead of $0,$ and $11111$ instead

of $1.$ If the receiver of the message uses $$major$-$

ity$$ decoding, what is the probability that the

message will be wrong when decoded? What

independence assumptions are you making?