0.095
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The bag contains 8 red marbles, 2 blue marbles, and 5 green marbles, making the total:
Since the marbles are drawn without replacement, the probability can be calculated step-by-step:
1. Probability of drawing the first green marble:
- P(G₁) = Number of green marbles / Total number of marbles
- P(G₁) = 5 / 15 = 1/3
2. Probability of drawing the second green marble after one green marble has already been drawn:
- P(G₂|G₁) = (Number of green marbles - 1) / (Total number of marbles - 1)
- P(G₂|G₁) = 4 / 14 = 2/7
3. Multiply these probabilities to find the combined probability of both events occurring:
- P(Both Green) = P(G₁) P(G₂|G₁)
- P(Both Green) = (1/3) (2/7)
- P(Both Green) = 2/21
4. Finally, convert this fraction to a decimal to the nearest thousandth:
- P(Both Green) ≈ 2 / 21 ≈ 0.095
Therefore, the probability that both marbles drawn will be green is approximately 0.095.
