# 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.