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Consider two bags containing 20 marbles. In each bag, 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 marble from the first bag and a striped marble from the second bag? Write your answer as a reduced fraction.(1 point)

1 answer

To find the probability of selecting a green marble from the first bag and a striped marble from the second bag, we will calculate each probability separately and then multiply them together.

  1. Probability of selecting a green marble from the first bag:

    • In the first bag, there are a total of 20 marbles, consisting of:
      • 5 red
      • 3 green
      • 2 yellow with stripes
      • 7 blue
      • 3 green with stripes
    • The total number of green marbles (both plain green and green with stripes) is \(3 + 3 = 6\).

    The probability of selecting a green marble from the first bag is: \[ P(\text{green from first bag}) = \frac{\text{number of green marbles}}{\text{total number of marbles}} = \frac{6}{20} = \frac{3}{10} \]

  2. Probability of selecting a striped marble from the second bag:

    • Similar to the first bag, the second bag also contains a total of 20 marbles consisting of the same distribution. The striped marbles consist of:
      • 2 yellow with stripes
      • 3 green with stripes
    • The total number of striped marbles is \(2 + 3 = 5\).

    The probability of selecting a striped marble from the second bag is: \[ P(\text{striped from second bag}) = \frac{\text{number of striped marbles}}{\text{total number of marbles}} = \frac{5}{20} = \frac{1}{4} \]

  3. Combined probability: To find the probability of both events happening (selecting a green marble from the first bag and a striped marble from the second bag), we multiply the two probabilities together: \[ P(\text{green from first bag and striped from second bag}) = P(\text{green from first bag}) \times P(\text{striped from second bag}) = \frac{3}{10} \times \frac{1}{4} = \frac{3 \times 1}{10 \times 4} = \frac{3}{40} \]

Thus, the probability of selecting a green marble from the first bag and a striped marble from the second bag is \(\frac{3}{40}\).

The final answer is: \[ \boxed{\frac{3}{40}} \]