Question

A bag contains

9

marbles:
2

are green,
2

are red, and
5

are blue. Omar chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that the first marble is green and the second is red? Write your answer as a fraction in simplest form.

Answer 1

For the first draw, if he has 9 marbles and 2 are green, the probability is 2/9. Without putting it back, 8 marbles are left, and he draws a red. Since there are 2 red of 8 marbles, the probability is 1/4. Now, multiply the two:
2/36
Simplify:
1/18
Hope this helps!

Answer 2

For the first marble chosen, the probability that the marble is green is 5/9. After the first choice, since she didn't put it back, there are 8 marbles left, of which 2 are red. So the probability of the second one being red is 2/8 = 1/4. Since the question is asking the probability of BOTH events happening, you multiply the two probabilities. So the answer is (5/9) * (1/4) = 5/36.
hope this helps