A bag contains 3 red marbles, 8 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be red?
First, we need to find the total number of marbles in the bag:
Total number of marbles = 3 + 8 + 2 = 13
Now, we need to find the number of ways to draw 2 red marbles out of the 3 red marbles:
Number of ways to draw 2 red marbles = 3C2 = 3
Next, we need to find the number of ways to draw 2 marbles out of the 13 marbles:
Number of ways to draw 2 marbles out of 13 = 13C2 = (13 x 12) / (2 x 1) = 78
Therefore, the probability of drawing 2 red marbles is:
3 / 78 = 1 / 26
So the exact probability that both marbles drawn will be red is 1/26 or approximately 0.0385.