Question

There is a bag filled with 3 blue, 4 red and 5 green marbles.

A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of exactly 1 red?

Answer 1

22.22%

Explanation:

If it is exactly a red, it means that it is removed on the first or second attempt, but only once, in this case it does not matter if it is on the first or second attempt because the marble is returned to the bag.

So suppose that on the first attempt red is drawn, the probability would be:

4 / (3 + 4 + 5) = 4/12 = 1/3

Now, on the second attempt, it is not to draw a red, it must be green or blue, so it would be:

(5 + 3) / (3 + 4 + 5) = 8/12 = 2/3

The final probability then is:

1/3 * 2/3 = 0.2222

that is, the probability is 22.22%