A bag contains 5 red marbles, 7 blue marbles and 2 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 blue?

Answer 1

The total number of marbles in the bag is 5 + 7 + 2 = 14.

The probability of drawing a blue marble on the first draw is 7/14 = 1/2.

After drawing a blue marble, there are 6 blue marbles left out of the remaining 13 marbles.

Therefore, the probability of drawing a blue marble on the second draw, given that a blue marble was already drawn, is 6/13.

To find the probability of both events happening, we multiply the probabilities together:

(1/2) * (6/13) = 6/26 = 3/13 ≈ 0.231 (rounded to the nearest 1000th)

So, the probability that both marbles drawn will be blue is approximately 0.231.