Question

Suppose a jar contains 13 red marbles and 33 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

7.5%

Explanation:

Although they tell us that they are held at the same time, there is no difference between taking out first and then another, because the marbles DO NOT have a replacement.

So the final probability would be:

Total marbles 13 + 33 = 46

The probability of drawing a red would be: 13/46, on the first attempt.

In the second half it would be: 12/45, because we have one less marble and I specify a red one.

Therefore, the final probability is the multiplication of both events, like this:

P = (13/46) * (12/45) = 0.075

In other words, the probability of this happening is 7.5%.