## baddinlol 2 years ago I can't get the right answer for this probability question

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

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

Ok sorry

5. zordoloom

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

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

numbers

9. zordoloom

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

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

13. zordoloom

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

14. zordoloom

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

15. zordoloom

and 5% will use dial up

yep

17. zordoloom

Okay, that would give you the data for 1 month

18. zordoloom

You want to continue doing this for 4 months.

But I must do the question using transition matrices

20. zordoloom

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

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

It would be set up a little differently.

How would i set it up?

28. zordoloom

The first row would include the percentages

29. zordoloom

sorry, column

30. zordoloom

and the next column would be the changes

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

32. zordoloom

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

33. zordoloom

So I would set up this matrix using a 4x4

Oh ok, thanks for your help =D

35. zordoloom

|dw:1351223751855:dw|

36. zordoloom

Just continue from here. Hope that somwhat helped