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I can't get the right answer for this probability question

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I must use transition matrices
The question is; an internet company has 80% of its customers on a dial plan and 20% of the cable plan
Can you just put the whole question out, instead of writing in small segments.

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Other answers:

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

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