A bag contains 6 red marbles, 3 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be red?

Answer 1

The total number of marbles in the bag is 6 + 3 + 5 = 14.

The probability of drawing a red marble on the first draw is 6/14.

After drawing a red marble on the first draw, there are now only 5 red marbles left out of a total of 13 marbles in the bag. Therefore, the probability of drawing a red marble on the second draw is 5/13.

After drawing two red marbles, there are now only 4 red marbles left out of a total of 12 marbles in the bag. Therefore, the probability of drawing a red marble on the third draw is 4/12.

To find the probability of all three marbles being red, we multiply the probabilities of each individual draw:

(6/14) * (5/13) * (4/12) = 120/2184 ≈ 0.0549

Therefore, the probability, to the nearest 1000th, that all three marbles drawn will be red is approximately 0.054.