A bag contains 7 red marbles, 3 blue marbles and 6 green marbles. If two marbles are drawn out of the bag, what is the probability to the nearest 10th of a percent, that both marbles drawn will be red?
To find the probability that both marbles drawn will be red, we need to find the total number of ways to draw 2 marbles out of the bag and the number of ways to draw 2 red marbles.
Total number of marbles = 7 red + 3 blue + 6 green = 16
Number of ways to draw 2 marbles out of 16 = 16C2 = (16 * 15) / (2 * 1) = 120
Number of ways to draw 2 red marbles = 7C2 = (7 * 6) / (2 * 1) = 21
Probability = Number of ways to draw 2 red marbles / Total number of ways to draw 2 marbles
Probability = 21 / 120 = 0.175 = 17.5%
Therefore, the probability to the nearest 10th of a percent that both marbles drawn will be red is 17.5%.