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

Question

Assume that you have 6 red balls and 7 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

Katie,

Because the order with which it appears is not necessary we can try two different ways to answer the same question 

probability that the first ball is blue = 6/13

probability that the second is not blue given that the first ball is blue = 7/12 - a blue's taken out

∴ probability that exactly one blue ball is chosen (6/13)(7/12)

probability that the first is not blue = 7/13

probability that the second ball is blue given that the first ball is not blue = 6/12 - one red ball's taken out 

∴ probability that exactly one blue ball is chosen (6/12)(7/13)

I hope this helps Katie