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A bag contains 5 red marbles, 7 blue marbles and 2 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?
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A bag contains 55 red marbles, 77 blue marbles and 22 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 55 red marbles, 77 blue marbles and 22 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 number of marbles: Determine the total number of marbles in the bag.\newlineThe bag contains 55 red marbles, 77 blue marbles, and 22 green marbles. To find the total, add these numbers together.\newlineTotal marbles = 55 red + 77 blue + 22 green\newlineTotal marbles = 1414
  2. Calculate probability of drawing green marble: Calculate the probability of drawing one green marble. Since there are 22 green marbles and 1414 total marbles, the probability of drawing one green marble on the first draw is: Probability of first green marble == Number of green marbles // Total number of marbles Probability of first green marble =214= \frac{2}{14}
  3. Calculate probability of second green marble: Calculate the probability of drawing a second green marble after one has already been drawn.\newlineAfter one green marble has been drawn, there is now 11 green marble left and the total number of marbles in the bag is 1313. The probability of drawing the second green marble is:\newlineProbability of second green marble == Number of remaining green marbles // New total number of marbles\newlineProbability of second green marble =113= \frac{1}{13}
  4. Calculate combined probability: Calculate the combined probability of both events happening.\newlineTo find the probability of both events happening (drawing two green marbles in a row), multiply the probabilities of each individual event.\newlineCombined probability = Probability of first green marble ×\times Probability of second green marble\newlineCombined probability = (2/14)×(1/13)(2 / 14) \times (1 / 13)\newlineCombined probability = 2/1822 / 182
  5. Simplify combined probability: Simplify the combined probability.\newlineSimplify the fraction 2182\frac{2}{182} to its lowest terms.\newlineCombined probability = 191\frac{1}{91}
  6. Convert probability to percentage: Convert the probability to a percentage.\newlineTo convert the probability to a percentage, multiply by 100100.\newlinePercentage probability = Combined probability ×100\times 100\newlinePercentage probability = (1/91)×100(1 / 91) \times 100
  7. Calculate percentage to nearest tenth: Calculate the percentage to the nearest tenth of a percent.\newlinePerform the division to find the percentage.\newlinePercentage probability 1.0989%\approx 1.0989\%\newlineTo the nearest tenth of a percent, this is approximately 1.1%1.1\%.

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