Question 1137840
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Part A


Make a table that looks something like this
<img src = "https://i.imgur.com/vTVypk6.png">
The stuff in red along the rows is the first stock picked while the stuff in blue along the columns is the second stock picked. 
Each cell in the form (x,y) is a result of picking one of each color. 


Eg: row 2, column 4 has (I2, U1) in it from red I2 along the left hand side and the blue U1 up top. You can think of it as a game of battleship in terms of how you locate a ship you want to target.


Mark out the main diagonal. I'm doing so in yellow highlighter
<img src = "https://i.imgur.com/zNFrylY.png">
This main diagonal is where you pick the same stock twice. This isn't possible, so we will ignore this diagonal and anything below it (the stuff below the diagonal is a symmetric copy of the stuff above the diagonal). The cells we ignore can be blotted out like so
<img src = "https://i.imgur.com/sbXXOCR.png">
The stuff that isn't covered up forms the sample space


<pre>
S = sample space 
S = set of all possible ways to pick 2 stocks
S = {(I1, I2),   (I1, I3),   (I1, U1),   (I1, U2),
                 (I2, I3),   (I2, U1),   (I2, U2),
                             (I3, U1),   (I3, U2),
                                         (U1, U2) }
</pre>
This formatting mimics the pattern in how the remaining ordered pairs show up in the table. Otherwise things could get a bit cluttered. The curly braces tell the reader "this is a set".


Extra info:
There are 4 items in row 1
There are 3 items in row 2
There are 2 items in row 3
There is 1 item in row 4
In total, there are 4+3+2+1 = 10 items in the sample space.

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Part B


A = event that investor picks two industrial stocks
A = set of all pairs (x,y) such that x and y are picked from {I1,I2,I3}
A = { (I1, I2),	(I1, I3), (I2, I3) }
We can see this by highlighting these cells below
<img src = "https://i.imgur.com/sFbPW1V.png">


There are 3 ways to get what we want out of 10 items total (sample space size)


The answer as a fraction is 3/10</font>