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?
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 :)
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?
To calculate the probability of drawing a green marble for each of the four possible outcomes, we need to consider the number of ways that outcome can occur and divide it by the total number of possible outcomes.
Here are the four different ways the game could end:
1. The first marble drawn is green.
- There is only one green marble, and there are a total of four marbles. So the probability of this outcome is 1/4.
2. The second marble drawn is green.
- This outcome can occur if the first marble drawn is not green (3 red marbles out of 4 left) and the second marble is green (1 green marble out of 3 left). So the probability of this outcome is (3/4) * (1/3) = 1/4.
3. The third marble drawn is green.
- This outcome can occur if the first two marbles drawn are not green (3 red marbles out of 4 left after the first draw, and 2 red marbles out of 3 left after the second draw) and the third marble is green (1 green marble out of 2 left). So the probability of this outcome is (3/4) * (2/3) * (1/2) = 1/4.
4. The fourth (last) marble drawn is green.
- This outcome can only occur if the first three marbles drawn are not green (3 red marbles out of 4 left after the first draw, 2 red marbles out of 3 left after the second draw, and 1 red marble out of 2 left after the third draw) and the fourth marble is green (1 green marble out of 1 left). So the probability of this outcome is (3/4) * (2/3) * (1/2) * (1/1) = 1/4.
Therefore, the probability of drawing a green marble for each of the four possible outcomes is 1/4 for each outcome.