Question

A bag has 5 red marbles, 6 green marbles, 4 yellow marbles, 3 blue marbles, and 2 purple marbles.

What is the probability of randomly selecting a green marble from the bag. Express your answer as a fraction in simplified form.

(1 point)

Answer 1

To find the probability of randomly selecting a green marble from the bag, we first need to determine the total number of marbles in the bag.

The total number of marbles can be calculated as follows:

- Red marbles: 5
- Green marbles: 6
- Yellow marbles: 4
- Blue marbles: 3
- Purple marbles: 2

Now, we add these quantities together:

\[
5 + 6 + 4 + 3 + 2 = 20
\]

So, there are a total of 20 marbles in the bag.

Next, we identify the number of favorable outcomes for selecting a green marble. There are 6 green marbles in the bag.

The probability \( P \) of selecting a green marble is the ratio of the number of green marbles to the total number of marbles:

\[
P(\text{green marble}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{6}{20}
\]

Now we simplify the fraction \( \frac{6}{20} \):

To simplify, we find the greatest common divisor (GCD) of 6 and 20, which is 2.

Dividing the numerator and denominator by 2:

\[
\frac{6 \div 2}{20 \div 2} = \frac{3}{10}
\]

Thus, the probability of randomly selecting a green marble from the bag is:

\[
\boxed{\frac{3}{10}}
\]