A communication channel with binary input and three possible scenarios at the output is described as follows. The input to the channel is either 0 or 1 with equal probability. Then the output of the channel is erased with probability $0.1$, meaning the receiver does not receive anything, is flipped with probability $0.3$, and is error-free, meaning is equal to the input, with probability $0.6$. What is $P(0$ is transmitted $\mid 0$ is received)? SP. AS404