# Discrete Math Markov Chainws #2

## Discrete Math Markov ChainWS #2

Name Date Pd

At ReaganHigh School, wearing flip flops is very common. To determine if they should design and sell a Raiders Teal flip flop, the Booster Club conducts a survey and found that if a student wears flip flops on a given day, there is an82% probability that he/she will wear flip flops the next day. If a student does notwear flip flops on a given day, there is a 9% probability that he/she willwear flip flops the next day.

1.)Draw a digraph representing this situation.

2.)Set up the transition matrix [T] representing this situation. (order = Flops, Not Flops)

3.)What does T12 represent?

4.)What does [T]512 represent?

5.)Find the steady state equilibrium. Write a sentence to describe what this indicates.

6.)Based on this, do you think the Booster Club should sell Raiders Teal flip flops? Explain.

Your family hosts a summer party. Your mother is very serious about her landscaping and insists that guests walk only on the pathways. Your Aunt Dotty Dash has a very short attention span and does not stay in the same spot for long. She also is very social – wanting to see everyone – and randomly chooses an exit pathway every 10 minutes.

7.)Draw a digraph representing this situation.

8.)Set up the transition matrix [T] representing this situation. (order = Hot Tub, Pool, House)

9.)What does T23 represent?

10.)How long is a cycle?

11.)What does [T]631 represent?

12.)If Aunt Dotty Dash started the party in the House, what is the probability that she is at the Pool in 1 hour? Using [T], exponents, and subscripts, show how you got this.

13.)Over the course of the long party, where is Dotty least likely to be found? Explain.

At summer camp, the girls’ bunkhouse is laid out as shown below.

14.)Draw a digraph representing this situation.

15.)Set up the transition matrix [T] representing this situation. (order = A, B, C, D)

16.)How long is a transition from one stage to the next?

17.)What does T32 represent?

18.)What is the probability that the skunk will be in cabin D after 2 minutes? Using [T], exponents, and subscripts, show how you got this.

19.)What is the probability that the skunk will be in cabin B after ½ hour? Using [T], exponents, and subscripts, show how you got this.

20.)In the long run, which Cabin would you want to be in? Explain.