## baddinlol Group Title I can't get the right answer for this probability question one year ago one year ago

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

3. zordoloom Group Title

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

Ok sorry

5. zordoloom Group Title

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?

7. zordoloom Group Title

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

numbers

9. zordoloom Group Title

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

12. zordoloom Group Title

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

13. zordoloom Group Title

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

14. zordoloom Group Title

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

15. zordoloom Group Title

and 5% will use dial up

yep

17. zordoloom Group Title

Okay, that would give you the data for 1 month

18. zordoloom Group Title

You want to continue doing this for 4 months.

But I must do the question using transition matrices

20. zordoloom Group Title

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

23. zordoloom Group Title

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 $\left(\begin{matrix}0.471875 \\ 0.28203125\end{matrix}\right)$

26. zordoloom Group Title

It would be set up a little differently.

How would i set it up?

28. zordoloom Group Title

The first row would include the percentages

29. zordoloom Group Title

sorry, column

30. zordoloom Group Title

and the next column would be the changes

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

32. zordoloom Group Title

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

33. zordoloom Group Title

So I would set up this matrix using a 4x4

Oh ok, thanks for your help =D

35. zordoloom Group Title

|dw:1351223751855:dw|

36. zordoloom Group Title

Just continue from here. Hope that somwhat helped