For a binary nonsymmetric channel we have Py$|$x $(0|1)=0\mathrm{.}1$ and Py$|$x $(1|0)=0\mathrm{.}2$ where x is the

transmitted digit and y is the received digit. Assume that Px $(0)=0\mathrm{.}4.$

$$ Determine Py $(0)$ and Py $(1)$

$$ What is the probability that only $0$s will be in the output for an input sequence of $10$ digits?

$$ What is the probability that eight $1$s and two $0$s will be in the output for an input sequence of

$10$ digits?

$$ What is the probability that at least five $0$s will be in the output for an input sequence of $10$

digits?