A bag contains 5 blacks balls and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and red balls are pi...

A bag contains 5 blacks balls and 3 red balls. Two balls are picked at random without replacement. What is the probability that a black and red balls are picked?

Answer Details

There are 5 black balls and 3 red balls in the bag, so there are a total of 8 balls. When two balls are picked at random without replacement, there are (8 choose 2) = 28 ways of doing so. To pick a black ball and a red ball, we can pick one black ball from the 5 available, and one red ball from the 3 available. There are (5 choose 1) = 5 ways to pick one black ball, and (3 choose 1) = 3 ways to pick one red ball. By the multiplication principle, there are a total of 5 × 3 = 15 ways to pick a black ball and a red ball. Therefore, the probability of picking a black ball and a red ball is 15/28.