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

1 answer

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:

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

  1. 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:

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