Question

Suppose that there is a black urn containing nine black balls and three yellow balls and there is a yellow urn containing six black balls and six yellow balls. An experiment consists of selecting at random a ball from the black urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball.

Required:
a. Construct a tree diagram showing the probabilities associated with this problem. Write a probability on each branch (6 branches).
b. Find the probability that the second ball is yellow.

Answer 1

See Annex for tree diagram and all probabilities

b) P(2y) = 0,329

Explanation:

a) Attached

b) Probability of the second ball is yellow P(2y) is equal to the probability of the second ball is yellow given that the first one is black ( 0,204 ) plus the probability f the second ball is yellow given that the first one is yellow ( 0,125)

P(2y) = 0,204 + 0,125

P(2y) = 0,329