anonymous 3 years ago I can't get the right answer for this probability question

1. anonymous

I must use transition matrices

2. anonymous

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

3. anonymous

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

4. anonymous

Ok sorry

5. anonymous

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

6. 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?

7. anonymous

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

8. anonymous

numbers

9. anonymous

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

10. anonymous

Oh no, they represent probablities

11. anonymous

if you divide them by 100 i suppose

12. anonymous

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

13. anonymous

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

14. anonymous

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

15. anonymous

and 5% will use dial up

16. anonymous

yep

17. anonymous

Okay, that would give you the data for 1 month

18. anonymous

You want to continue doing this for 4 months.

19. anonymous

But I must do the question using transition matrices

20. anonymous

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

21. anonymous

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

22. anonymous

I multiplied that by itself 4 times

23. anonymous

So far, it looks somewhat correct. You are missing

24. anonymous

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

25. anonymous

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

26. anonymous

It would be set up a little differently.

27. anonymous

How would i set it up?

28. anonymous

The first row would include the percentages

29. anonymous

sorry, column

30. anonymous

and the next column would be the changes

31. anonymous

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

32. anonymous

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

33. anonymous

So I would set up this matrix using a 4x4

34. anonymous

Oh ok, thanks for your help =D

35. anonymous

|dw:1351223751855:dw|

36. anonymous

Just continue from here. Hope that somwhat helped