Point masses and tail of a mixed distribution

Let $X$ be a random variable with the distribution function

$$F(x)=\begin{cases}0, & x<0,\ \dfrac14+\dfrac{4x-x^2}{8}, & 0\le x<2,\ 1, & x\ge2.\end{cases}$$

Then $P(X=0)+P(X=1.5)+P(X=2)+P(X\ge1)$ equals