A bag contains 2 red marbles, 7 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be blue?
There are a total of 14 marbles in the bag. The probability of drawing a blue marble on the first draw is 7/14 (since there are 7 blue marbles out of 14 total marbles). After drawing one marble, there are only 13 marbles left in the bag. If the first marble drawn was blue, there are now only 6 blue marbles left out of 13 total marbles. Therefore, the probability of drawing a second blue marble after the first one was blue is 6/13.
To find the probability of both events happening (drawing a blue marble on the first draw AND drawing another blue marble on the second draw), we multiply the probabilities together:
(7/14) x (6/13) = 21/91
Therefore, the exact probability of drawing two blue marbles out of the bag is 21/91.