Chapter 10, Problem 1EA

If a teacher is currently ill, what is the probability that he or she will retire during the fallowing year? What is the probability that be or she will be ill again in the following year?

To determine

The probability that when the teacher will retire during the provided year and also tell the probability of her to fall ill again.

Answer to Problem 1EA

Solution: The probability that when the teacher will retire during the provided year is 0.139 and also the probability of her to fall ill again is 0.055.

Explanation of Solution

Given: Consider the summary provided in the textbook.

Explanation:

By the summary provided in the textbook,

The Markov chain model for teacher retention has 8 states: Resigned, Retired, Decreased,

New, Continuing, On Leave, On Sabbatical, and III.

The transition matrix for the one-year period is provided as:

$\left[\begin{array}{ccccccccc}& \text{Resigned}& \text{Retired}& \text{Deceased}& \text{New}& \text{Continuing}& \text{On Leave}& \text{On}\text{Sabbatical}& \text{III}\\ \text{Resigned}& 1& 0& 0& 0& 0& 0& 0& 0\\ \text{Retired}& 0& 1& 0& 0& 0& 0& 0& 0\\ \text{Deceased}& 0& 0& 1& 0& 0& 0& 0& 0\\ \text{New}& 0.194& 0& 0& 0& 0.777& 0& 0& 0.033\\ \text{Continuing}& 0.040& 0.016& 0.002& 0& 0.896& 0.022& 0.007& 0.017\\ \text{On Leave}& 0.533& 0& 0& 0& 0.178& 0.289& 0& 0\\ \text{OnSabbatical}& 0& 0& 0& 0& 1& 0& 0& 0\\ \text{III}& 0& 0.139& 0& 0& 0.806& 0& 0& 0.055\end{array}\right]$

The entry that is in row 8 and column 2 of the transition matrix is 0.139.

So, the probability that the teacher will retire during the provided year is 0.139.

Also, it can be seen that the entry in the row 8 and column 8 of the transition matrix is 0.055.

Hence, the probability that the teacher will be ill again is 0.055.

Conclusion: The probability when the teacher will retire during the provided year is 0.139 and also the probability of her to fall ill again is 0.055.