A bag contains 8 red marbles, 4 blue marbles and 7 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be red?
There are a total of 19 marbles in the bag. The probability of drawing a red marble on the first draw is 8/19. After one red marble has been drawn, there are 7 red marbles left in the bag out of 18 total marbles. Therefore, the probability of drawing a red marble on the second draw, given that the first marble was red, is 7/18. Similarly, the probability of drawing a red marble on the third draw, given that the first two marbles were red, is 6/17.
To find the probability of all three marbles being red, we multiply the probabilities of each draw:
(8/19) * (7/18) * (6/17) = 0.0664
Therefore, the exact probability of drawing all three red marbles is 0.0664 or approximately 6.64%.