From a source, symbols 0 and 1 are transmitted independently of each other in proportion . Random noise may cause transmission failures: If a 0 was sent, 1:4 then a 1 will arrive at the sink with...

From a source, symbols 0 and 1 are transmitted independently of each other in proportion . Random noise may cause transmission failures: If a 0 was sent, 1:4 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) A 1 has arrived. What is the probability that a 1 had been sent?

(2) A 0 has arrived. What is the probability that a 1 had been sent?