You are watching two items posted for sale on eBay and bid $30 for the first and $20 for the second item. You estimate that you are going to win the first bid with probability 0.1 and the second bid with probability 0.2, and you assume that winning the two bids are independent events. Let X denote the random variable denoting the total amount of money you will spend on the two items.

a. List the sample space of all possible outcomes of winning or losing the two bids. (Draw a tree diagram.)
b. Find the probability of each outcome in the sample space. (Use the tree diagram.)
c. Find the probability distribution of X.
d. Find the mean of X.