Algebra question confusing

Question

A bag contains 10 marbles: 2 are green, 2 are red, and 6 are blue. Dan chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles he chooses are green? Write your answer as a fraction in simplest form.

Answer 1

First green: 2 / 20

Second green: 1 / 19

(1/ 10)(1 / 19)

1 / 190

Answer 2

Think of such problems as two events. Start by handling them separately.

There are 10 marbles. Two are green. On the first pick, the probability of picking a green is 2/10 or 1/5.

(Remember that a probability is always a fraction with the denominator representing all the possible outcomes and the numerator being the number of outcomes defined as a success.)

The second pick is slightly different because we have not replaced the one green. Therefore, we now have a total of nine marbles, of which only one is green. So the probability of selecting the one green is 1/9.

The method for finding the probability of two events both occurring is simply P(a) x P(b). In this case, 1/5 x 1/9, which is 1/45.

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