Question

Consider a jar containing 20 marbles. There are 5 red, 3 green, 2 yellow with stripes, 7 blue, and 3 green with stripes. What is the probability of selecting a green or striped marble? Write your answer as a reduced fractio

Answer 1

To find the probability of selecting a green or striped marble, we need to count the total number of green marbles and striped marbles, and then divide by the total number of marbles in the jar.

1. **Count the green marbles:**
- There are 3 green marbles.
- There are also 3 green marbles with stripes.

Total green marbles = 3 (green) + 3 (green with stripes) = 6 green marbles.

2. **Count the striped marbles:**
- The striped marbles include the 2 yellow striped marbles and the 3 green striped marbles.

Total striped marbles = 2 (yellow with stripes) + 3 (green with stripes) = 5 striped marbles.

3. **Count the unique green or striped marbles:**
- We have already counted green marbles that are also striped (the 3 green with stripes) in both groups.

To avoid double counting, we consider:
- Total green or striped marbles = (3 green) + (2 yellow striped) + (3 green striped) = 3 + 2 + 3 = 8 marbles.

4. **Total number of marbles:**
- The jar contains 20 marbles (5 red + 3 green + 2 yellow with stripes + 7 blue + 3 green with stripes).

Thus, the probability of selecting a green or striped marble is calculated as:

\[
\text{Probability} = \frac{\text{Number of green or striped marbles}}{\text{Total number of marbles}} = \frac{8}{20}
\]

5. **Reduce the fraction:**
- We can simplify \(\frac{8}{20}\) by dividing both the numerator and denominator by 4:

\[
\frac{8 \div 4}{20 \div 4} = \frac{2}{5}.
\]

Therefore, the probability of selecting a green or striped marble is:

\[
\boxed{\frac{2}{5}}.
\]