4.14 Matrices modeling contexts
Interactive practice questions
A website uploads two blog posts each day, one about social issues $\left(S\right)$(S) and the other about environmental concerns $\left(E\right)$(E).
Of the people who read a blog every day, $52%$52% of those that read about social issues on one day will read about social issues the next day. Also, $83%$83% of those that read about environmental concerns will also read about environmental concerns the next day.
Which of the following diagrams best represents this information?
Construct the transition matrix $T$T that represents the transitional probabilities between each state.
| E | S | ||||
|---|---|---|---|---|---|
| $T=$T= | $\editable{}$ | $\editable{}$ | E | ||
| $\editable{}$ | $\editable{}$ | S |
On a certain day, the website records that $800$800 people read blog $\left(E\right)$(E) while $550$550 people read $\left(S\right)$(S). Use this information to predict the number of readers that will read blog $\left(E\right)$(E) in $3$3 days time. Round your answer to the nearest whole number.
Each summer holidays the families of children in a school either stay at home (H) or go away on vacation (V).
The activities for the holidays change according to the below transition matrix.
Irene (I) and Larry (L) are playing chess. They each have an equal chance of winning the first game. If Irene wins, then she gains confidence and her chance of winning the next game becomes $70%$70%. If Larry wins, his chance of winning the next game is $60%$60%.
In the year 2003, there were $220000$220000 people living in Town A and $60000$60000 people in Town B. Each year, $5%$5% of the people in Town A move to Town B, and $23%$23% of the people in Town B move to Town A.