I have no idea how to approach the solution mathematically. Probability is one of my mathematical weaknesses. Instead, I created an Excel workbook with four worksheets. I started with a school with only two teachers and two classes, then three, four, and finally five teachers and classes. In each worksheet, I listed all the combinations and then used a formula in cell D3 to calculate the percentage of times the last teacher was successful dividing by the total number of combinations. In each case, the number was 50 percent. Since this was quite tedious to create as the number of classes and teachers grew, I considered writing a Python script for the actual problem with 10 classes and teachers, but I think the pattern will hold, so I will most likely not do this. Another interesting tidbit was that the last teacher either got to teach their class or the first teacher’s class.
I have attached my spreadsheet. Row five is a header row representing a particular teacher. In retrospect, these should have been labelled T1, T2, and so on. Then, rows following contain which class a teacher chose. So, for example in row 6, teacher 1 chooses class 1, and therefore all other teachers choose their correct class."
Rick,
Thursday, January 2, 2025
"I believe the answer is 50 percent.
I have no idea how to approach the solution mathematically. Probability is one of my mathematical weaknesses. Instead, I created an Excel workbook with four worksheets. I started with a school with only two teachers and two classes, then three, four, and finally five teachers and classes. In each worksheet, I listed all the combinations and then used a formula in cell D3 to calculate the percentage of times the last teacher was successful dividing by the total number of combinations. In each case, the number was 50 percent. Since this was quite tedious to create as the number of classes and teachers grew, I considered writing a Python script for the actual problem with 10 classes and teachers, but I think the pattern will hold, so I will most likely not do this. Another interesting tidbit was that the last teacher either got to teach their class or the first teacher’s class.
I have attached my spreadsheet. Row five is a header row representing a particular teacher. In retrospect, these should have been labelled T1, T2, and so on. Then, rows following contain which class a teacher chose. So, for example in row 6, teacher 1 chooses class 1, and therefore all other teachers choose their correct class."