A bag contains 8 blue and 2 red balls. Three balls are chosen at the same time at random from the bag.

What is the probability that exactly two of the balls are the same colour?

Answer:

24) C

We need to find out the probability of either 2 blue balls or 2 red balls.

Each of the scenarios has 3 possibilities.
That is, 2 red balls can be obtained by RRB, RBR, BRR
2 blue balls can be obtained by BBR, BRB, RBB

Probability of 2 red balls = 2/10 x 1/9 x 8/8 x 3 = 42/720
Probability of 2 red balls = 8/10 x 7/9 x 2/8 x 3 = 336/720

Probability of 2 balls being the same colour = 42/720 + 336/720 = 384/720 = 8/15