Question

an urn contains ten marbles, of which five are green, two are blue, and three are red. three marbles are to be drawn from the urn, one at a time without replacement. what is the probability that exactly one of the marbles drawn will be green?

Answer 1

The probability that exactly one of the marbles drawn will be green is 1/2.

Step-by-step explanation:

To find the probability that exactly one of the marbles drawn will be green, we need to consider the different ways this can happen.

First, we can select a green marble on the first draw and any non-green marble on the second and third draws. There are 5 green marbles and 5 non-green marbles remaining after the first draw, so the probability of this happening is (5/10) * (5/9) * (4/8) = 1/6.

Second, we can select a non-green marble on the first draw, a green marble on the second draw, and a non-green marble on the third draw. There are 5 green marbles and 5 non-green marbles remaining after the first draw, so the probability of this happening is (5/10) * (5/9) * (4/8) = 1/6.

Finally, we can select a non-green marble on the first draw, a non-green marble on the second draw, and a green marble on the third draw. There are 5 green marbles and 5 non-green marbles remaining after the first draw, so the probability of this happening is (5/10) * (4/9) * (5/8) = 1/6.

Adding up these probabilities, the total probability that exactly one of the marbles drawn will be green is 1/6 + 1/6 + 1/6 = 3/6 = 1/2.