11. Suppose that an urn contains two black balls and one red ball. You draw a ball from the urn at random. If you draw a red ball on the first try, it is returned to the urn along with two additional red balls. But if you draw a black ball on the first try, it will be returned to the urn along with one black ball and two red balls. A second draw is then made.
a. What is the probability that a red ball will be drawn on the first draw?
b. What is the probability that a red ball will be drawn on both the first and second draws?
c. What is the probability that a black ball will be drawn on the first draw?
d. What is the probability that a black ball will be drawn on both the first and the second draws?
12. Suppose an urn contains three black balls and two red balls. And suppose you draw two balls without replacement.
a. What is the probability that you will draw a red ball in your first draw?
b. What is the probability that you will draw both red balls in two draws?
c. What is the probability that you will draw a black ball in your first draw?
d. What is the probability that you will draw two black balls in two draws?