Answer to Question #44949 in Statistics and Probability for Pranav V K

Question

A communication channel transmits the digits 0 and 1. However due to static noise, the digit transmitted is incorrectly received with probability 0.2
Suppose we want to transmit an important message consisting of one binary digit. To reduce the chance of error, we transmit 00000 instead of 0
And 11111 instead of 1. If the receiver of the message uses majority decoding , what is the probability that the message will be incorrectly decoded.
( by majority decoding we mean that the message is decoded as 0 if there are
At least 3 zeros in the message received and as 1 otherwise.)