A bag contains 5 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 red?
There are a total of 16 marbles in the bag, so the probability of drawing a red marble on the first draw is 5/16. After one red marble is drawn, there are only 4 red marbles left in the bag, out of a total of 15 marbles. Therefore, the probability of drawing a second red marble is 4/15. To find the probability of both events happening (drawing two red marbles), we multiply the probabilities:
(5/16) x (4/15) = 1/12
So the probability of drawing two red marbles out of the bag is 1 in 12, or approximately 0.0833 to the nearest 1000th.