Show all the necessary steps as clear as possible ( \( 15 \% \) )
1) In a binary communication system, a ' 0 ' and a ' 1 ' is transmitted with probability 0.6 and 0.4 respectively. Due to an error occurring in the communication system, a ' 0 ' becomes a ' 1 ' with a probability of 0.1 , and a ' 1 ' becomes a ' 0 ' with a probability of 0.08 . Find
a) The probability of receiving a ' 1 '
b) The probability of receiving a ' 0 '
c) The probability that a ' 1 ' was transmitted when the received message is ' 1 '.