Numerical Problem (Graph) Contract Sales Across Companies

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p1nkm4n

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Hi everyone, this is the third and the last of my query for this time. Posting the question below:

13.jpg

I understand the graph is giving the sales percentage for each company out of the industry total. Company B winning 36 out of 450 contracts in Year 7 means 8%. I am not sure on how to move forward from this point or if this is related to probability. Any help is highly appreciated! Thank you for reading.

P.S. Moderators, please kindly move this thread to the relevant section if this is a probability related question.
 
p1nkm4n said:
Hi everyone, this is the third and the last of my query for this time. Posting the question below:

View attachment 10372

I understand the graph is giving the sales percentage for each company out of the industry total. Company B winning 36 out of 450 contracts in Year 7 means 8%. I am not sure on how to move forward from this point or if this is related to probability. Any help is highly appreciated! Thank you for reading.

P.S. Moderators, please kindly move this thread to the relevant section if this is a probability related question.
Click to expand...

They tell you to look for a pattern in the graphs of A and B. Do you see anything interesting there?
 
From the graph it appears that, for the previous year, company A won 12 contracts while company B won 6. That is, company A won twice as many contracts as B. The simplest estimate we can make is that this continues into the next year. If B won 36 contracts this year, we would expect company A to win 72.
 
p1nkm4n said:
They're both mirrored to each other?
Click to expand...

Correct. When one went up, the other went down by the same amount, which means that the sum of the two has always been constant.

Now, they are asking you to find A pattern, and assume that THAT pattern continues, which is a stretch. One never makes such assumptions in real life and says that they are certain. Rather, we look for reasons that the pattern might continue.

They might have some other pattern in mind. But this is what I think they probably mean.
 
p1nkm4n said:
They're both mirrored to each other?
Click to expand...
A lot of math is learning how important it is to formulate questions and observations in a useful way. In that sense, math is a language that stresses precision.

Yes, the year-to-year changes in number of contracts awarded are of identical magnitude but differ in sign. As Dr. Peterson says, that relationship entails that the sum of the number of contracts awarded to the two companies has been constant for several years. As Halls says, in several years, the one company was awarded half as many contracts as the other.

There is very little data to go on. In real life, you would look for more information before making a judgment on such skimpy data.

Here, I'd probably go with the pattern supported by more evidence as what the test makers want as an answer. Again, I feel this is a poor problem. There is not much mathematical basis for assuming either pattern will recur exactly. It is more about guessing what the people who dreamed these problems up want as an answer.
 
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