Symbols 0 and 1 are transmitted independently from each other in proportion \(1: 4\). Random noise may cause transmission failures: If a 0 was sent, then a 1 will arrive at the sink with probability 0.1 . If a 1 was sent, then a 0 will arrive at the sink with probability 0.05 (figure).

(1) What is the probability that a received symbol is ' 1 '?

(2) ' 1 ' has been received. What is the probability that ' 1 ' had been sent?

(3) ' 0 ' has been received. What is the probability that ' 1 ' had been sent?