A bag holds 8 yellow marbles and 5 orange marbles. How many and what color marbles would you add to the bag so that the probability of picking a yellow marble is 2/3?

Answer 1

lets add x yellow marbles

so (x+8)/(x+13) = 2/3
3x + 24 = 2x + 26
x = 2

must add 2 yellows

or

lets add y orange marbles
8/(y+13) = 2/3
2y + 26 = 24
2y = -2
y = -1

or we could take out 1 orange marble
Proof:
yellow = 8
orange = 4
total = 12
prob of yellow = 8/12 = 2/3