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

- anonymous

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

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- anonymous

I must use transition matrices

- anonymous

The question is; an internet company has 80% of its customers on a dial plan and 20% of the cable plan

- anonymous

Can you just put the whole question out, instead of writing in small segments.

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## More answers

- anonymous

Ok sorry

- anonymous

No worries, it just helps to refer to one post instead of searching each post for parts of a question.

- 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

Alright, does the question use numbers, or just percentages?

- anonymous

numbers

- anonymous

I mean, you just listed that there are 80% and 20%, do these percentages represent any numbers?

- anonymous

Oh no, they represent probablities

- anonymous

if you divide them by 100 i suppose

- anonymous

Thats fine, just use any number then. It would make the calculations easier.

- anonymous

So, say you have a total of 100 customers. 80% use dial up and 20% use cable

- anonymous

now after 1 month, 20% of the dial up customers will use the cable

- anonymous

and 5% will use dial up

- anonymous

yep

- anonymous

Okay, that would give you the data for 1 month

- anonymous

You want to continue doing this for 4 months.

- anonymous

But I must do the question using transition matrices

- anonymous

Thats fine, Do you know what a transition matrix is?

- anonymous

I tried setting up \[\left[\begin{matrix}0.8 & 0.2 \\ 0.05& 0.95\end{matrix}\right]\]

- anonymous

I multiplied that by itself 4 times

- anonymous

So far, it looks somewhat correct. You are missing

- anonymous

And then multiplied it by\[\left(\begin{matrix}0.8 \\ 0.2\end{matrix}\right)\]

- anonymous

And i got \[\left(\begin{matrix}0.471875 \\ 0.28203125\end{matrix}\right)\]

- anonymous

It would be set up a little differently.

- anonymous

How would i set it up?

- anonymous

The first row would include the percentages

- anonymous

sorry, column

- anonymous

and the next column would be the changes

- anonymous

Oh so columns have to add upto 100 (in terms of percentages)?

- anonymous

kinda, Its more like each row includes the number of variables. In this case there are 4 months.

- anonymous

So I would set up this matrix using a 4x4

- anonymous

Oh ok, thanks for your help =D

- anonymous

|dw:1351223751855:dw|

- anonymous

Just continue from here. Hope that somwhat helped

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