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A bag contains 3 red marbles, 7 blue marbles and 8 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1oooth, that all three marbles drawn will be blue? Answer:

A bag contains 33 red marbles, 77 blue marbles and 88 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 11oooth, that all three marbles drawn will be blue?\newlineAnswer:

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Q. A bag contains 33 red marbles, 77 blue marbles and 88 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 11oooth, that all three marbles drawn will be blue?\newlineAnswer:
  1. Calculate Total Marbles: First, we need to determine the total number of marbles in the bag.\newlineTotal marbles = 33 red + 77 blue + 88 green = 1818 marbles.
  2. Calculate Probability of First Blue Marble: Next, we calculate the probability of drawing one blue marble from the bag.\newlineThe probability of drawing the first blue marble is the number of blue marbles divided by the total number of marbles.\newlineProbability of first blue marble = Number of blue marbles / Total number of marbles = 718\frac{7}{18}.
  3. Calculate Probability of Second Blue Marble: After drawing one blue marble, there are now 66 blue marbles left and 1717 marbles in total.\newlineThe probability of drawing a second blue marble is now the number of remaining blue marbles divided by the new total number of marbles.\newlineProbability of second blue marble = Number of remaining blue marbles / New total number of marbles = 617\frac{6}{17}.
  4. Calculate Probability of Third Blue Marble: After drawing a second blue marble, there are now 55 blue marbles left and 1616 marbles in total.\newlineThe probability of drawing a third blue marble is now the number of remaining blue marbles divided by the new total number of marbles.\newlineProbability of third blue marble = Number of remaining blue marbles / New total number of marbles = 516\frac{5}{16}.
  5. Calculate Probability of Drawing Three Blue Marbles: To find the probability of all three events happening in sequence (drawing three blue marbles in a row), we multiply the probabilities of each event.\newlineProbability of drawing three blue marbles in a row = Probability of first blue marble ×\times Probability of second blue marble ×\times Probability of third blue marble = (7/18)×(6/17)×(5/16)(7/18) \times (6/17) \times (5/16).
  6. Perform Multiplication to Find Probability: Now we perform the multiplication to find the probability.\newlineProbability = (718)×(617)×(516)=210(18×17×16)=2104896(\frac{7}{18}) \times (\frac{6}{17}) \times (\frac{5}{16}) = \frac{210}{(18 \times 17 \times 16)} = \frac{210}{4896}.
  7. Simplify Fraction and Round Probability: Finally, we simplify the fraction and round it to the nearest thousandth.\newlineProbability (rounded to the nearest thousandth) = 2104896≈0.043\frac{210}{4896} \approx 0.043 (rounded to three decimal places).

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