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Glencoe Algebra 2, p. 204

PT: Markov Chains

RW: Health/Flu

Due to a flu epidemic, the school nurse estimates that 30% of the students who are well today will be sick tomorrow and 50% of the students who are sick today will be well tomorrow.

a)   Write a transition matrix to show this situation.

b)   If 80% of the student population is well today, predict what percent will be sick tomorrow.

c)   If you are sick Monday predict what percent chance that you will be still be sick on Wednesday.

Glencoe Algebra 2, p. 200

PT: Markov Chain

RW: Psychologist/Mice in a Maze

A psychologist notes the behavior of mice at a certain point in a maze.  For any particular trail, 70% of the mice that went right on the previous trail will go right on this trial, and 60% of those that went left on the previous trial will go right on this trial.  The following transition matrix can represent this information:

T =

 R L R 0.7 0.3 L 0.6 0.4

Suppose 50% of the mice went right on the first trial.  This is represented by the following probability matrix.

P=

 R L 0.50 0.50

a)      Make a prediction for the second trial.

b)      Make a prediction for the third trial.  Explain your reasoning.

Key to Problem Bank:

 M: Misconception PT: Probability Topic RW: Real World Topic