What is the probability that exactly one blue ball is chosen?

Question

Assume that you have 5 red balls and 6 blue balls from which randomly to select two without replacement.
(1) What is the probability that exactly one blue ball is chosen?

(2) What is the probability that the second ball is blue given that at least one of the balls is blue?

Answer 1

In this case, there are 11 balls, 5 red, and 6 blue.

 

So the chance of drawing one blue ball will be 6 divided by 11, or 54.5%

 

Once a blue ball has been drawn, there will be 5 red balls, and 5 blue balls.

 

So, the chance of drawing a blue ball will 5 divided by 10, or 50%

 

The probability of the two events is the product of the two values, or 0.545 x 0.5 = 0.275 = 27.5%