On the way to school, Hendrik passes three traffic lights. For years he noted how often each light was red. He came to the following conclusions:
light A: 50% chance of red
light B: 30% chance of red
light C: 10% chance of red
Determine the probability distribution that shows the number of times that Hendrik has to stop on the way to school.
For now I found that P(x=0)=0.315 ($P(\overline{A})$ * $P(\overline{B})$ * $P(\overline{C})$) and P(x=3)=0.015 ($P(A)$ * $P(B)$ * $P(C)$). But I can't find P(x=1) and P(x=2)
Edit: These are the answers in my book
$
P(x=0)=0.315;
P(x=1)=0.485;
P(x=2)=0.185;
P(x=3)=0.015;
$
Best Answer
There is an interesting way to arrange the computation.
Let $f(x) = (.5 + .5 x) (.7 + .3 x) (.9 + .1 x)$.
If we expand $f(x)$, we get $$f(x) = 0.315\, +0.485 x+0.185 x^2+0.015 x^3$$
Notice a resemblance to your problem?