# Probability question

#### dzim

##### New member
I'm having trouble helping my daughter on this question.
"In Box A there are 3 black and 5 green marbles. In Box B there are 4 black marbles and 6 green marbles. One marble is taken from each box. What is the probability that both marbles are the same colour?" The answer in the textbook is 21/40 but we are not sure how to get that. Any help would be appreciated.

#### MarkFL

##### Super Moderator
Staff member
Hello, and welcome to FMH!

I would first look at the probability that both marbles are black...we'll call this event B:

$$\displaystyle P(B)=\frac{3}{8}\cdot\frac{4}{10}=\frac{3}{20}$$

Next, let's look at the probability that both marbles are green...we'll call this event G:

$$\displaystyle P(G)=\frac{5}{8}\cdot\frac{6}{10}=\frac{3}{8}$$

Now, if event X is that both marbles are the same color, then:

$$\displaystyle P(X)=P(B\text{ OR }G)=\frac{3}{20}+\frac{3}{8}=\frac{21}{40}$$

Does that make sense?

#### dzim

##### New member
sure does. Thanks