A bag contains 3 red marbles 7 blue marbles and 4 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 green
There are a total of 14 marbles in the bag. The probability of drawing a green marble on the first draw is 4/14 (since there are 4 green marbles out of 14 total marbles). After one green marble is drawn, there are 13 marbles left in the bag, including 3 green marbles. So the probability of drawing a green marble on the second draw, after one has already been drawn, is 3/13.
To find the probability of both events happening (drawing a green marble on the first draw AND drawing a green marble on the second draw), we multiply the two probabilities:
(4/14) x (3/13) = 12/182
Simplifying this fraction, we get:
12/182 = 6/91
Therefore, the probability, to the nearest 1000th, that both marbles drawn will be green is 0.066.