I need help with this.

Question

A bag contains 10 marbles: 2 are green, 6 are red, and 2 are blue. Tony 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

The probability that an event (A) occurs is:

P(A) = n(A)/n(S)

where n(A) = the number of ways event A can occur and n(S) = the total number of possible events that can occur. In a bag of 10 marbles, n(S) = 10. There are 2 green marbles, so n(A) = 2 and the probability of picking a green marble on the first pick is:

P(green1) = 2/10 = 1/5

If you don't put the marble back, then there are 9 marbles for the second pick and n(S) = 9. There is only one green marble left so n(A) = 1. The probability of picking a green marble on the second pick is:

P(green 2) = 1/9

The probability of picking 2 green marbles without replacement is:

P(2 green) = P(green1)·P(green2) = 1/5 · 1/9 = ____?