cenario: You have marbles of 2 colors, red and blue. You put one red and one blue marble in a bag and take one at random. The probability of getting a red marble is obviously 50%. But then you add 5 more blue marbles in the bag and take one at random again. The probability of getting red for that attempt alone is obviously 1/7, but how do I calculate the overall probability of getting a red marble at least once through both attempts whereas each attempt has a different probability?
Attempt 1: 2 marbles, 1 red, 1 blue
Attempt 2: 7 marbles, 2 red, 5 blue
Attempt 3: 10 marbles, 3 red, 7 blue
It doesn't take a mathematician to figure out the probabilities for each individual attempt, but in the given scenario, how is the overall probability calculated?
By the way, I already figured it out using pictures: 105/140 chance. But is there some formula I can use for such math problems like above?