A bag contains 4 red marbles, 7 blue marbles and 8 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that both marbles drawn will be green?
There are a total of 19 marbles in the bag, so the probability of drawing a green marble on the first draw is 8/19. After one green marble is removed from the bag, there are 18 marbles left, including 7 green marbles. So the probability of drawing a green marble on the second draw, given that the first marble drawn was green, is 7/18. To find the probability of both events happening (drawing two green marbles in a row), we multiply the probabilities:
(8/19) x (7/18) = 56/342
To convert this fraction to a percentage, we divide the numerator by the denominator and multiply by 100:
56/342 ≈ 0.164 = 16.4%
Therefore, the probability, to the nearest 10th of a percent, of drawing two green marbles in a row is 16.4%.