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.
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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.
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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.
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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.
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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:
\[ \text{Probability} = \frac{\text{Number of green or striped marbles}}{\text{Total number of marbles}} = \frac{8}{20} \]
- 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:
\[ \boxed{\frac{2}{5}}. \]