Box a contains 8 black marbles and 5 white marbles box b contains 8 black marbles and 9 white marbles a marble is randomly drawn from box a and its color is recorded. The marble is then placed in box b and a marble is randomly drawn from box b and is color recorded.

a. sketch a probability tree

b. find the probability of each possible outcome

c. find the probability that a black marble is drawn on the second draw

d. find the probability that at least one of the marbles drawn is white.

e. find the probability that the second marble is black given that the first marble is white