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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Asked Oct 11, 2019
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6.12 Buying on eBay 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.
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6.12 Buying on eBay 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.

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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.
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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.

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Expert Answer

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:

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Total Amount Second bid First bid $30 $20 loss loss win win P(W)-0.1 P(L) 0.9 P(W)-0.2 P(L)=0.8

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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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Sample space Probability P(WW-0.1*0.2=0.02 P(WL) 0.1*0.8=0.08 P(LW) 0.9*0.2-0.18 P(LL)-0.9*0.8=0.72 ww WL LW LL

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