Question

What is the sum of the probabilities of the favorable outcomes and the unfavorable outcomes, p(x=1)+p(x≠1)p(x=1)+p(x≠1)?

Answer 1

What's the sample space? Are we talking about rolling a die or what?

Anyway, if we call the probability $p(x=1) = x$, then $p(x\neq 1) = 1-x$

So, the expression becomes

$x + (1-x)x + (1-x) = x + x - x^2 + 1 - x = -x^2+x+1$