Charity fair: assigning probabilities
This task is designed to assess how well students understand assigning probabilities and expected value.
The task looks at a ‘Lucky Dip’ game designed to raise money for charity. There are three barrels, each contains equal numbers of red, green, white and black balls. The game costs 25¢ to enter and players take a ball at random from each barrel. If each of the balls is the same colour then the player wins $5. The task is to work out if the game will be successful in raising money for charity. An extension task asks students for ways in which the game can be altered to raise more money.
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.