anonymous
  • anonymous
I can't get the right answer for this probability question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I must use transition matrices
anonymous
  • anonymous
The question is; an internet company has 80% of its customers on a dial plan and 20% of the cable plan
anonymous
  • anonymous
Can you just put the whole question out, instead of writing in small segments.

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anonymous
  • anonymous
Ok sorry
anonymous
  • anonymous
No worries, it just helps to refer to one post instead of searching each post for parts of a question.
anonymous
  • anonymous
An internet company has 80% of its customers on a dial plan and 20% of the cable plan. They decide to bring out a deal which the market manager estimates each month, 20% of the customers on the dial up plan will change to the cable modem plan and 5% of the customers on the cable plan will change to the dial up plan. No customers will stop using the company. After four months, what proportion of the present customers will now be on the dial up plan?
anonymous
  • anonymous
Alright, does the question use numbers, or just percentages?
anonymous
  • anonymous
numbers
anonymous
  • anonymous
I mean, you just listed that there are 80% and 20%, do these percentages represent any numbers?
anonymous
  • anonymous
Oh no, they represent probablities
anonymous
  • anonymous
if you divide them by 100 i suppose
anonymous
  • anonymous
Thats fine, just use any number then. It would make the calculations easier.
anonymous
  • anonymous
So, say you have a total of 100 customers. 80% use dial up and 20% use cable
anonymous
  • anonymous
now after 1 month, 20% of the dial up customers will use the cable
anonymous
  • anonymous
and 5% will use dial up
anonymous
  • anonymous
yep
anonymous
  • anonymous
Okay, that would give you the data for 1 month
anonymous
  • anonymous
You want to continue doing this for 4 months.
anonymous
  • anonymous
But I must do the question using transition matrices
anonymous
  • anonymous
Thats fine, Do you know what a transition matrix is?
anonymous
  • anonymous
I tried setting up \[\left[\begin{matrix}0.8 & 0.2 \\ 0.05& 0.95\end{matrix}\right]\]
anonymous
  • anonymous
I multiplied that by itself 4 times
anonymous
  • anonymous
So far, it looks somewhat correct. You are missing
anonymous
  • anonymous
And then multiplied it by\[\left(\begin{matrix}0.8 \\ 0.2\end{matrix}\right)\]
anonymous
  • anonymous
And i got \[\left(\begin{matrix}0.471875 \\ 0.28203125\end{matrix}\right)\]
anonymous
  • anonymous
It would be set up a little differently.
anonymous
  • anonymous
How would i set it up?
anonymous
  • anonymous
The first row would include the percentages
anonymous
  • anonymous
sorry, column
anonymous
  • anonymous
and the next column would be the changes
anonymous
  • anonymous
Oh so columns have to add upto 100 (in terms of percentages)?
anonymous
  • anonymous
kinda, Its more like each row includes the number of variables. In this case there are 4 months.
anonymous
  • anonymous
So I would set up this matrix using a 4x4
anonymous
  • anonymous
Oh ok, thanks for your help =D
anonymous
  • anonymous
|dw:1351223751855:dw|
anonymous
  • anonymous
Just continue from here. Hope that somwhat helped

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