   SEARCH HOME Math Central Quandaries & Queries  Question from Ninoshka: Liu and Michi plan to sign up for a drawing class next term. Drawing is offered during the first 4 periods of the day, and students are assigned randomly to class. What is the probability that Liu and Michi will have drawing together? Hi,

I'm going to create a 2-digit code where the first digit tells you which period Liu has drawing and the second digit tells you which period Michi has drawing. So for example if Liu has drawing in the second period and Michi has drawing the fourth period I will write 2,4. Likewise if Lui has drawing in the third period and Michi has drawing in the first period I will write 3,1. Now I am going to create a table of all of the possibilities for the class assignments. The rows in the table list the possibilities for Liu and the columns list the possibilities for Michi.

1
2 3
4
1

2

2,4
3
3,1

3

I filled in two of the cells in the table, 2,4 and 3,1. You can fill in the remainder of the table.

When Liu and Michi are assigned periods at random they will end up in one of the 16 cells in the table and each cell is equally likely. How many of the cells have them both taking drawing in the same period? What is the probability that Liu and Michi will have drawing together?

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.