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A bag contains 5 red marbles, 7 blue marbles and 3 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 blue?
Answer:

A bag contains 55 red marbles, 77 blue marbles and 33 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 blue?\newlineAnswer:

Full solution

Q. A bag contains 55 red marbles, 77 blue marbles and 33 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 blue?\newlineAnswer:
  1. Determine Total Marbles: Determine the total number of marbles in the bag.\newlineAdd the number of red, blue, and green marbles together.\newline55 red + 77 blue + 33 green = 1515 total marbles.
  2. Calculate First Blue Probability: Calculate the probability of drawing the first blue marble.\newlineSince there are 77 blue marbles out of 1515 total marbles, the probability of drawing a blue marble first is 715\frac{7}{15}.
  3. Calculate Second Blue Probability: Calculate the probability of drawing a second blue marble after the first one has been drawn.\newlineNow there are 66 blue marbles left and only 1414 marbles total. The probability of drawing a second blue marble is 614\frac{6}{14}.
  4. Multiply Probabilities: Multiply the probabilities from Step 22 and Step 33 to find the probability of both events occurring.\newline(715)×(614)=42210=15(\frac{7}{15}) \times (\frac{6}{14}) = \frac{42}{210} = \frac{1}{5}.
  5. Convert to Percentage: Convert the probability into a percentage. 15=0.2\frac{1}{5} = 0.2 and as a percentage, this is 20%20\%.
  6. Round to Nearest Tenth: Round the percentage to the nearest tenth of a percent. 20%20\% is already at the nearest tenth of a percent, so no further action is needed.

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