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A bag contains 3 red marbles, 5 blue marbles and 6 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1oth of a percent, that both marbles drawn will be green? Answer:

A bag contains 33 red marbles, 55 blue marbles and 66 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 11oth of a percent, that both marbles drawn will be green?\newlineAnswer:

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Q. A bag contains 33 red marbles, 55 blue marbles and 66 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 11oth of a percent, that both marbles drawn will be green?\newlineAnswer:
  1. Determine total marbles: Determine the total number of marbles in the bag.\newlineThe bag contains 33 red marbles, 55 blue marbles, and 66 green marbles. To find the total, add these numbers together.\newlineTotal marbles = 33 red + 55 blue + 66 green = 1414 marbles.
  2. Calculate green marble probability: Calculate the probability of drawing one green marble. Since there are 66 green marbles out of a total of 1414, the probability of drawing one green marble is 614\frac{6}{14}.
  3. Calculate second green marble probability: Calculate the probability of drawing a second green marble after one has already been drawn.\newlineAfter drawing one green marble, there are now 55 green marbles left and a total of 1313 marbles in the bag. The probability of drawing a second green marble is now 513\frac{5}{13}.
  4. Calculate both events probability: Calculate the probability of both events happening together (drawing two green marbles in a row).\newlineTo find the probability of both events happening, multiply the probabilities of each event.\newlineProbability of both green marbles = (614)×(513)(\frac{6}{14}) \times (\frac{5}{13}).
  5. Perform multiplication: Perform the multiplication to find the probability.\newlineProbability of both green marbles = (614)×(513)=(6×514×13)=30182(\frac{6}{14}) \times (\frac{5}{13}) = (\frac{6 \times 5}{14 \times 13}) = \frac{30}{182}.
  6. Simplify fraction: Simplify the fraction to its lowest terms. \newline30182\frac{30}{182} can be simplified by dividing both the numerator and the denominator by 22.\newlineSimplified probability = 1591\frac{15}{91}.
  7. Convert to percentage: Convert the probability to a percentage.\newlineTo convert to a percentage, divide 1515 by 9191 and then multiply by 100100.\newlinePercentage = (1591)×100(\frac{15}{91}) \times 100.
  8. Perform division and multiplication: Perform the division and multiplication to find the percentage. \newlinePercentage = (1591)×100≈16.4835%(\frac{15}{91}) \times 100 \approx 16.4835\%.
  9. Round to nearest tenth: Round the percentage to the nearest tenth of a percent.\newlineRounded percentage = 16.5%16.5\%.

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