Question

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 1

P(2blue) = 8/10 * 7/9

P(2red) = 2/10 * 1/9

Either-or probabilities are found by adding the individual probabilities.

Answer 2

you can basically get two of each color 3 diff ways

2 red = (2/10 * 1/9 * 8/8)+(8/10 * 2/9 * 1/8)+(2/10 * 8/9 * 1/8) = 3(16/720)

2 blue = (8/10 * 7/9 * 2/8)+(8/10 * 2/9 * 7/8)+(2/10 * 8/9 * 7/8) = 3(112/720)

at the end you jsut add these together and get the final %

3(16/720) + 3(112/720) = 8/15