Lottery: systematic listing
This task assesses how well students understand systematic listing and expected value.
The task features a proposal for a lottery game. Players must pay a $1 fee to enter the lottery. They are given a card showing the numbers 1 to 6. Players cross through two numbers of their choosing. A bag contains balls with the numbers from 1 to 6. At the end of the week, two balls are drawn from the bag. Every player who has chosen the same two numbers as shown on the balls wins a cash prize of $10. The task is to evaluate if the game will be good for raising money.
There are a number of different approaches to the task, one of which is to use systematic listing and expected value.
This task is from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. A full rubric is given for the task, together with examples of student work and suggestions for helping students overcome misconceptions. Further information on the collection is given here.