Question

a bag contains exactly 15 marbles of which 3 are red, 5 are blue, and 7 are green. the marbles are chosen at random and removed one at a time from the bag until all of the marbles are removed. one colour of marble is the first to have 0 remaining in the bag. what is the probability that this colour is red?

Answer 1

The probability of the first color to have 0 remaining in the bag being red is 0.13333

Step-by-step explanation:

To find the probability that the first color to have 0 remaining in the bag is red, we need to calculate the probability of drawing all the other colors before drawing the last red marble.

There are a total of 15 marbles in the bag, with 3 red marbles. After each draw, the total number of marbles decreases by 1. So for the first draw, the probability of drawing a red marble is 3/15.

For the second draw, there are 14 marbles remaining in the bag, with 3 red marbles.

So the probability of not drawing a red marble is 11/14.

Continuing this pattern, the probability of drawing all the other colors before drawing the last red marble is the product of the probabilities for each draw.

So the probability of the first color to have 0 remaining in the bag being red is:

Probability = (3/15) * (11/14) * (10/13) * ... * (5/9) = 0.13333