There is a bag with 3 green marbles, and 2 red marbles. What is the probability of the 1st marble being green OR the 2nd marble being green?
I first made use of the formula: P(A or B) = P(A) + P(B) - P(A and B)
From this I found that: P(1st green) = 3/5
And that: P(2nd green) = P(2nd green|1st green) + P(2nd green|1st red)
So: P(1st green or 2nd green) = (3/5) + (1/2) + (3/4) - (3/10) = 31/20
I know this is incorrect because the probability is greater than 1. What am I doing wrong?
Your expression for the probability that the second is green is incorrect. Indeed, the probability that any particular slot is green is $\frac 35$.
Specifically, you need to weight each term in your sum by the probability of being in that situation. That is to say $$P(2nd\, green) = P(2nd\, green|1st \,green)\times P(first \;green) + P(2nd\, green|first\, red)\times P(first\,red)$$