I am thinking about one question, the result seems weird, but I could not figure out where I went wrong.
I have two random Bernoulli variables $X$ and $Y$.
$=P(Y=1|X=1)P(X=1)+P(Y=1|X=0)(1 - P(X=1))$
It seems that a probabilities of one Bernoulli random variable is always a linear function of another Bernoulli random variable no matter of what! This does not make sense to me. Could you please let me know where I went wrong?