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

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

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Q. A bag contains 55 red marbles, 33 blue marbles and 66 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be green?\newlineAnswer:
  1. Determine total number: Determine the total number of marbles in the bag.\newlineThe bag contains 55 red marbles, 33 blue marbles, and 66 green marbles. To find the total, we add these numbers together.\newline55 (red) + 33 (blue) + 66 (green) = 1414 (total marbles)
  2. Calculate first green probability: Calculate the probability of drawing the first green marble.\newlineThe probability of an event is the number of favorable outcomes divided by the total number of outcomes. Since there are 66 green marbles and 1414 total marbles, the probability of drawing a green marble first is:\newlineProbability of first green marble = Number of green marbles / Total number of marbles\newlineProbability of first green marble = 614\frac{6}{14}
  3. Calculate second green probability: Calculate the probability of drawing a second green marble after the first one has been drawn.\newlineAfter drawing one green marble, there are now 55 green marbles left and 1313 marbles in total. The probability of drawing a second green marble is:\newlineProbability of second green marble = Number of remaining green marbles / Total remaining marbles\newlineProbability of second green marble = 513\frac{5}{13}
  4. Calculate combined probability: Calculate the combined probability of both events happening consecutively.\newlineTo find the probability of both events happening one after the other, we multiply the probabilities of each event.\newlineCombined probability = Probability of first green marble ×\times Probability of second green marble\newlineCombined probability = (614)×(513)(\frac{6}{14}) \times (\frac{5}{13})
  5. Simplify combined probability: Simplify the combined probability.\newlineWe can simplify the fraction by multiplying the numerators together and the denominators together.\newlineCombined probability = (6×5)/(14×13)(6 \times 5) / (14 \times 13)\newlineCombined probability = 30/18230 / 182\newlineThis fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 22.\newlineCombined probability = 30/2/182/230/2 / 182/2\newlineCombined probability = 15/9115 / 91

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