Question

A bag contain 3 blue marbles, 4 red marbles, and 2 green marbles. What is the probability of picking a red or a green marble?

Answer 1

To find the probability of picking a red or a green marble from the bag, we first need to determine the total number of marbles.

The bag contains:
- 3 blue marbles
- 4 red marbles
- 2 green marbles

Calculating the total number of marbles:
\[
\text{Total marbles} = 3 \text{ (blue)} + 4 \text{ (red)} + 2 \text{ (green)} = 9 \text{ marbles}
\]

Next, we count the number of favorable outcomes for picking a red or a green marble. The number of red marbles is 4, and the number of green marbles is 2.

Adding these together gives:
\[
\text{Number of red or green marbles} = 4 \text{ (red)} + 2 \text{ (green)} = 6
\]

Now, we can compute the probability of picking either a red or a green marble using the formula for probability:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{9}
\]

To simplify this fraction:
\[
\frac{6}{9} = \frac{2}{3}
\]

Thus, the probability of picking a red or a green marble is \(\frac{2}{3}\).