Answered

A bag contains 8 red marbles, 2 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the
nearest 1000th, that both marbles drawn will be green?
Answer



Answer :

mhanifa

0.095

==================

The bag contains 8 red marbles, 2 blue marbles, and 5 green marbles, making the total:

  • 8 + 2 + 5 = 15 marbles

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.

Other Questions