Question

A bag of 10 Marbles has the following composition:

Red – 3

Green – 4

Blue – 2

Yellow – 1

What is the Compound Probability of reaching in at random and extracting 3 Red Marbles in a row? Calculate as INDEPENDENT EVENTS.

Answer 1

Explanation:

Since the events are independent, we can use the multiplication rule of probability.

The probability of selecting a red marble on the first draw is 3/10.

After one red marble is drawn, there are 2 red marbles left in the bag and 9 total marbles. So the probability of selecting a red marble on the second draw, given that a red marble was already selected on the first draw, is 2/9.

Similarly, after two red marbles are drawn, there is only 1 red marble left in the bag and 8 total marbles. So the probability of selecting a red marble on the third draw, given that two red marbles were already selected on the first two draws, is 1/8.

Therefore, the compound probability of selecting 3 red marbles in a row is:

(3/10) x (2/9) x (1/8) = 1/120

So the probability of selecting 3 red marbles in a row is 1/120 or approximately 0.0083.