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?Answer:
Q. 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?Answer:
Determine total number of marbles: Determine the total number of marbles in the bag.The bag contains 5 red marbles, 7 blue marbles, and 2 green marbles. To find the total, add these numbers together.Total marbles = 5 red + 7 blue + 2 greenTotal marbles = 14
Calculate probability of drawing green marble: Calculate the probability of drawing one green marble. Since there are 2 green marbles and 14 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 =142
Calculate probability of second green marble: Calculate the probability of drawing a second green marble after one has already been drawn.After one green marble has been drawn, there is now 1 green marble left and the total number of marbles in the bag is 13. The probability of drawing the second green marble is:Probability of second green marble = Number of remaining green marbles / New total number of marblesProbability of second green marble =131
Calculate combined probability: Calculate the combined probability of both events happening.To find the probability of both events happening (drawing two green marbles in a row), multiply the probabilities of each individual event.Combined probability = Probability of first green marble × Probability of second green marbleCombined probability = (2/14)×(1/13)Combined probability = 2/182
Simplify combined probability: Simplify the combined probability.Simplify the fraction1822 to its lowest terms.Combined probability = 911
Convert probability to percentage: Convert the probability to a percentage.To convert the probability to a percentage, multiply by 100.Percentage probability = Combined probability ×100Percentage probability = (1/91)×100
Calculate percentage to nearest tenth: Calculate the percentage to the nearest tenth of a percent.Perform the division to find the percentage.Percentage probability ≈1.0989%To the nearest tenth of a percent, this is approximately 1.1%.