Question

There is a bag filled with 6 blue and 5 red 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 getting 2 of the same colour?

Answer 1

61/121

Explanation:

With replacement, the different outcomes have probabilities ...

P(r, r) = (5/11)(5/11) = 25/121

P(r, b) = (5/11)(6/11) = 30/121

P(b, r) = (6/11)(5/11) = 30/121

P(b, b) = (6/11)(6/11) = 36/121

These outcomes are mutually exclusive, so the probability of any combination of them is the sum of their individual probabilities.

P(x, x) = P(r, r) +P(b, b) = 25/121 +36/121 = 61/121

The probability of two the same color is 61/121.