Task# Stay or Switch?

Illustrative MathematicsVaries

The purpose of this task is for students to find the theoretical probability of an event by systematically recording all of the possible outcomes in the sample space and identifying those that correspond to the event. The tricky thing about the problem is that most people assume that it doesn't matter if they stay or switch, thinking that because there are two choices, the chances of getting the points is '50-50.' This would be correct if it is equally likely that the 10,000 points is in either of the two boxes, but this is not the case. However, the correct probability can be easily deduced from the uniform probability model applied (appropriately) to the initial situation or approximated by carrying out a simulation.