Question

A bag contains marbles of four different colors:
8 blue
24 red
16 green
4 yellow

​The probability of picking either a green or a red marble is

Answer 1

To find the probability of picking either a green or a red marble from the bag, we first need to determine the total number of marbles in the bag and the number of favorable outcomes (green and red marbles).

1. **Count the marbles by color:**
- Blue marbles: 8
- Red marbles: 24
- Green marbles: 16
- Yellow marbles: 4

2. **Calculate the total number of marbles:**
\[
\text{Total number of marbles} = 8 + 24 + 16 + 4 = 52
\]

3. **Calculate the number of favorable outcomes (green and red marbles):**
\[
\text{Number of green marbles} = 16
\]
\[
\text{Number of red marbles} = 24
\]
\[
\text{Total favorable outcomes} = 16 + 24 = 40
\]

4. **Calculate the probability of picking either a green or a red marble:**
\[
P(\text{green or red}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of marbles}} = \frac{40}{52}
\]

5. **Simplify the fraction:**
\[
\frac{40}{52} = \frac{10}{13}
\]

Thus, the probability of picking either a green or a red marble is \(\frac{10}{13}\).