Question

A bag contains 8 red marbles, 7 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be green?

Answer 1

The probability of drawing a green marble on the first draw is 2/17, since there are 2 green marbles out of a total of 17 marbles in the bag.
After the first green marble is drawn, there will be 1 green marble left out of 16 marbles.
Therefore, the probability of drawing a second green marble after the first green marble has been drawn is 1/16.
To find the probability of both events happening, we multiply the probabilities:
P(drawing two green marbles) = P(drawing a green marble on the first draw) x P(drawing a green marble on the second draw after a green marble was already drawn)

P(drawing two green marbles) = (2/17) x (1/16)

P(drawing two green marbles) = 1/136

Therefore, the exact probability of drawing two green marbles out of the bag is 1/136.