You draw 2 marbles from a bag containing 3 blue marbles, 2 green marbles,
and 5 red marbles without replacement. What is the probability of drawing a
red marble and then a green marble?
1/10
1/9
1/2
13/18
To find the probability of drawing a red marble and then a green marble, we need to calculate the probability of each event separately and then multiply them together.
First, let's calculate the probability of drawing a red marble on the first draw. There are 10 marbles in total, and 5 of them are red. Therefore, the probability of drawing a red marble on the first draw is 5/10.
After drawing a red marble on the first draw, there are now 9 marbles left in the bag. Out of these 9 marbles, 2 of them are green. So the probability of drawing a green marble on the second draw, after drawing a red marble on the first draw, is 2/9.
To find the probability of both events occurring, we multiply their probabilities together:
(5/10) * (2/9) = 10/90 = 1/9
Therefore, the probability of drawing a red marble and then a green marble is 1/9.
So, the correct answer is 1/9.
10 marbles total, so
P(red,green) = 5/10 * 2/9