A bag contains 8 red marbles, 6 blue marbles and 3 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be blue?
There are a total of 17 marbles in the bag. The probability of drawing a blue marble on the first draw is 6/17. After the first marble is drawn, there are 16 marbles left in the bag, including 5 blue marbles. So the probability of drawing a blue marble on the second draw, given that the first marble was blue, is 5/16.
To find the probability of both events occurring (drawing a blue marble on the first AND second draw), we multiply the probabilities:
(6/17) x (5/16) = 15/272
Therefore, the probability, to the nearest 1000th, that both marbles drawn will be blue is 0.055.