The diagram says that, if the input is 0, the output will be 0 with probability \(\displaystyle 1- \epsilon_1\) and 1 with probability \(\displaystyle \epsilon_1\) but if the input is 1 the output will be 0 with probability \(\displaystyle \epsilon_2\) and 1 with probability \(\displaystyle 1- \epsilon_2\).

We are also given that the probability the input will be 0 is p and the probability the input will be 1 is 1- p. What is the probability the output will be 0? That can happen in two ways: the input was 0 and the output was 0 or the input was 1 and the output was 0.

**Given** that the input was 0 what is the probability the output is 0? Multiply that by p. **Given** that the input was 1 what is the probability the output is 0 ? Multiply that by 1- p. Then add those two numbers.