A bag contains 4 red marbles, 6 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 blue?
The total number of marbles in the bag is 4 + 6 + 2 = 12.
The probability of drawing a blue marble on the first draw is 6/12 = 1/2.
After drawing a blue marble, there will be 5 blue marbles and 11 total marbles left in the bag.
The probability of drawing another blue marble on the second draw is 5/11.
Therefore, the probability of drawing two blue marbles in a row is:
(1/2) * (5/11) = 5/22
So, the exact probability that both marbles drawn will be blue is 5/22.