Neo is offered to choose between three boxes that look identical. The first box contains 11 red pills and 9 blue pills, the second box has 2 red pills and 18 blue pills, and the third box has 16 red pills and 4 blue pills. Neo randomly chooses a box and takes one pill out.
I have tried taking the probability of getting 4 reds in each box and adding them together but that didn't work. I figured since its impossible for the 2nd box to have 4 red pills you would add 0 but I'm not sure.
Your answer should be $P(1st)+P(2nd)+P(3rd)$.
You aren't exactly adding the probabilities, because you have to multiply by $\frac{1}{3}$, as there is only a $\frac{1}{3}$ chance he chooses each box.
But you are correct in $P(2nd)=0$.
Consider posting your work so we can see where, if anywhere, you went wrong.