# 6.12 Buying on eBay You are watching two items posted forsale on eBay and bid \$30 for the first and \$20 for the seconditem. You estimate that you are going to win the first bidwith probability 0.1 and the second bid with probability 0.2,and you assume that winning the two bids are independentevents. Let X denote the random variable denoting thetotal amount of money you will spend on the two items. a. List the sample space of all possible outcomes ofwinning or losing the two bids. (Draw a tree diagram.)b. Find the probability of each outcome in the samplespace. (Use the tree diagram.)c. Find the probability distribution of X.d. Find the mean of X.

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Step 1

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Step 2

a)

The first outcome in sample space is WW, here first W represents the winning of first bid and second W represents the winning of second bid. Other outcomes are WL, LW, and LL. In WL the first W represents the winning of first bid and second L represents the loosing of second bid and in LW in that first L represents the loosing of first bid and second W represents the winning of second bid and LL in that first L represents the loosing of first bid and second L represents the loosing of second bid.

Thus, the possible sample space is {WW, WL, LW, LL}.

Tree diagram:

Step 3

b)

The outcomes of the sample space is {WW, WL, LW, LL}.

Here, the probability of winning of first bid is 0.1 and winning of second bi...

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