Question

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?

Answer 1

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.