Question

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

Answer 1

I must use transition matrices

Answer 2

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

Answer 3

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

Answer 4

Ok sorry

Answer 5

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

Answer 6

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?

Answer 7

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

Answer 8

numbers

Answer 9

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

Answer 10

Oh no, they represent probablities

Answer 11

if you divide them by 100 i suppose

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

and 5% will use dial up

Answer 16

yep

Answer 17

Okay, that would give you the data for 1 month

Answer 18

You want to continue doing this for 4 months.

Answer 19

But I must do the question using transition matrices

Answer 20

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

Answer 21

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

Answer 22

I multiplied that by itself 4 times

Answer 23

So far, it looks somewhat correct. You are missing

Answer 24

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

Answer 25

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

Answer 26

It would be set up a little differently.

Answer 27

How would i set it up?

Answer 28

The first row would include the percentages

Answer 29

sorry, column

Answer 30

and the next column would be the changes

Answer 31

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

Answer 32

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

Answer 33

So I would set up this matrix using a 4x4

Answer 34

Oh ok, thanks for your help =D

Answer 35

Just continue from here. Hope that somwhat helped