Question

A bag contains 9 marbles: 2 are green, 2 are red, and 5 are blue. Yoko chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are green? Write your answer as a fraction in simplest form.

Answer 1

Answer: 1/36

Step-by-step explanation: To find the probability of picking a green marble and picking another green marble, it's important to understand that once Yoko chooses the first marble, it's not replaced which means that there are fewer marbles in the bag.

This means that the outcome of the first event affects the outcome of the second event which means that these are dependent events.

When finding the probability of two dependent events, we first find the probability of each event and then multiply the probabilities.

Let's first find the probability of choosing one green marble.

Since there are 2 green marbles are 9 total marbles, the probability of choosing a green marble is 2/9.

Next we find the probability of choosing another green marble. Remember that the first marble was not put back in the jar which means that there are 8 total marbles in the bag.

Since there is only 1 green marble left and 8 of them are in the bag, the probability of choosing another green one is 1/8.

Now to find the probability of choosing a green marble, not replacing it, and choosing another green marble, we multiply $(\frac{2}{9}) (\frac{1}{8})$.

Image provided.

Therefore, the probability of choosing a green marble, not replacing it, and choosing another green marble is 1/36.