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TIA A.1.05 Solution

Posted 01-22-2009 at 03:47 PM by rrbest
Updated 01-23-2009 at 01:18 AM by rrbest

The TIA videos helped me solve this problem, but in the process I developed a method which I think is simplified. Here is the problem:

5. There are three major newspapers in the city of Crobizon: the Globe, the Herald, and the
Phoenix. The Phoenix is distributed freely, but the Globe and Herald cost money. On a recent
day, sales of the newspapers were as follows:

(i) 25% of people didnít read any newspaper
(ii) 25% of people read the Globe and 29% read the Herald
(iii) 40% of people read the Phoenix
(iv) 9% of people read both the Globe and the Herald
(v) 3% of people read all 3 papers

What percentage of people read the Phoenix and also read exactly one of the other two papers?

Here is a picture I drew of the three scenarios. Red is Globe, Blue is Herald, and Green is Phoenix.

This image includes the easy steps of this problem, completing parts i, iv, and v.

Now it gets tricky because you feel like you don't have enough information. TIA started using x and y, but I believe its easier to solve the problem without that stuff. Here's how I did it.

1. We know that P[G u H u Ph] = .75 because we know .25 didn't read any papers.

2. P[G] = .25, P[H]=.29, P[Ph]=.4

The area we need to know is those squares with the question marks.

(.25)+(.29-.06-.03)= .45

What I did there was add those who read Globe, then those who read Herald, I then subtracted those who read both so there were no duplicates. We have P[G u H].

Now I add in phoenix

.45 + (.4-.03) = .82

I was only able to subtract the mid section because it is all we know, and I'm left with duplicates of both the parts that I need to know. However, because we know the entire space is .75, I can subtract .75 to get the combined area of both '?'s.

82-.75 = .07

Now to show the entire equation it is

.25+.(29-.03-.06)+(.40-.03)-(.75) = 0.07
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  1. Old Comment
    Very nice--I like that. My only complaint is with the color choices: if you are going to call one set G, and color one set green, I think it would be slightly easier if they match.
    Posted 01-23-2009 at 07:50 AM by daaaave daaaave is online now
  2. Old Comment
    Oh haha, good call on the coloring. I actually only colored them because it looks weird if they are all black and its harder to get a visual of the different sections. As mentioned, I think I slightly prefer rounded rectangles to perfect rectangles when using only black
    Posted 01-23-2009 at 01:58 PM by rrbest rrbest is offline

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