# Penalty shoot-out

Purpose

The purpose of this activity is to engage students in running an experiment to determine a probability and compare this with the results of similar practical situations.

Achievement Objectives
S3-3: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.
Description of Mathematics

The background knowledge and skills that should be established before and/or during this activity are outlined in the diagram below:

Click to show example questions for each heading

This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.

Activity

When a football player takes a penalty shot, they may aim at the left, the right or the centre of the goal. The goalie might leap to defend the left, the right or the centre of the goal. Run an experiment to simulate 52 penalty goals.

In the 2015 U20 FIFA world cup quarter finals, some of the games went to penalty shoot-outs. In these shoot outs, there were a total of 52 penalty shots, 35 of which were successful. Compare the results of your simulation with the results of the 2015 FIFA world cup quarter finals.

Assumptions to make:

• The player taking the shot and the goalie each choose one of the three possible targets at random.
• If the goalie defends the correct target, they will make a successful save.
• If the goalie does not defend the correct target, a goal will be scored.