A bag contains 7 red marbles, 2 blue marbles and 3 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 7+2+3=12.
The probability of drawing a blue marble on the first draw is 2/12.
After the first marble is drawn, there are 11 marbles remaining in the bag, including 1 blue marble out of 2 remaining.
So the probability of drawing a second blue marble is 1/11.
To find the probability of both events happening (drawing two blue marbles), we multiply the probabilities:
P(drawing two blue marbles) = (2/12) x (1/11)
= 1/66
Therefore, the exact probability that both marbles drawn will be blue is 1/66.