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A bag contains 5 red marbles, 6 blue marbles and 7 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10ooth, that both marbles drawn will be green? Answer:

A bag contains 55 red marbles, 66 blue marbles and 77 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1010ooth, that both marbles drawn will be green?\newlineAnswer:

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Q. A bag contains 55 red marbles, 66 blue marbles and 77 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1010ooth, that both marbles drawn will be green?\newlineAnswer:
  1. Calculate Total Marbles: Determine the total number of marbles in the bag.\newlineThe bag contains 55 red marbles, 66 blue marbles, and 77 green marbles.\newlineTotal number of marbles = 5+6+7=185 + 6 + 7 = 18 marbles.
  2. Calculate Probability of First Green Marble: Calculate the probability of drawing one green marble.\newlineSince there are 77 green marbles out of 1818 total marbles, the probability of drawing one green marble is:\newlineP(first green)=Number of green marblesTotal number of marbles=718.P(\text{first green}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{7}{18}.
  3. Calculate Probability of Second Green Marble: Calculate the probability of drawing a second green marble after one has already been drawn.\newlineAfter drawing one green marble, there are now 66 green marbles left and 1717 marbles in total.\newlineP(second green∣first green)=Number of green marbles leftTotal number of marbles left=617.P(\text{second green} | \text{first green}) = \frac{\text{Number of green marbles left}}{\text{Total number of marbles left}} = \frac{6}{17}.
  4. Calculate Combined Probability: Calculate the combined probability of both events happening (drawing two green marbles in a row).\newlineThe combined probability is the product of the probabilities of each individual event.\newlineP(both green)=P(first green)×P(second green | first green)=718×617P(\text{both green}) = P(\text{first green}) \times P(\text{second green | first green}) = \frac{7}{18} \times \frac{6}{17}.
  5. Perform Multiplication: Perform the multiplication to find the probability. P(both green)=718×617=42306P(\text{both green}) = \frac{7}{18} \times \frac{6}{17} = \frac{42}{306}.
  6. Simplify Fraction: Simplify the fraction to its lowest terms.\newline42306\frac{42}{306} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 66.\newlineP(both green)=(42÷6)(306÷6)=751P(\text{both green}) = \frac{(42 \div 6)}{(306 \div 6)} = \frac{7}{51}.
  7. Convert to Decimal: Convert the probability to a decimal to find the nearest thousandth.\newlineP(both green)=751≈0.137P(\text{both green}) = \frac{7}{51} \approx 0.137 (rounded to the nearest thousandth).

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