Question

A game has a box containing four marbles - three red and one green. The player draws one marble at a time without replacement until the green marble is drawn. After that, the game is over.
The game ends in four different ways. What is the probability of drawing a green marble for each of these possible outcomes?

Answer 1

green on first try = 1/4

green on second try:
red first = 3/4
then green = 1/3
so
3/4 * 1/3 = 1/4

green on third try
red first = 3/4
red second = 2/3
green third = 1/2
3/4 * 2/3 * 1/2 = 1/4

green o fourth try
red first = 3/4
red second = 2/3
red third = 1/2
green fourth = 1/1
would you believe 1/4 again :)

Answer 2

There is a shooting game that consists of 10 targets. The player must use a bow to hit all the targets in order to win a prize. What is the probability of hitting all 10 targets if the player has 15 arrows?