Question

Suppose a jar contains 14 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

To find the probability that both marbles drawn are red, you can use the concept of conditional probability.

First, let's calculate the probability of drawing the first red marble:
Probability of drawing the first red marble = (Number of red marbles) / (Total number of marbles) = 14 / (14 + 33) = 14/47

Now, since we're drawing two marbles at the same time, the total number of marbles decreases by 1 after the first marble is drawn. So, for the second marble to also be red:
Probability of drawing the second red marble = (Number of remaining red marbles) / (Total remaining marbles) = (14 - 1) / (47 - 1) = 13/46

Now, to find the probability that both events happen (both marbles are red), you multiply these probabilities together because they are independent events:

Probability (both marbles are red) = Probability of first red marble * Probability of second red marble = (14/47) * (13/46)

Calculating this:

Probability (both marbles are red) ≈ 0.0963 or approximately 9.63%

So, the probability that both marbles drawn are red is approximately 9.63%.