Investigating Probability Concepts of Secondary Pre-service Teachers in a Game Context

participants. 
 
 
DICE 1 
 
 
1 
2 
3 
4 
5 
6 
DICE
 2
 
1 
0 
1 
2 
3 
4 
5 
2 
1 
0 
1 
2 
3 
4 
3 
2 
1 
0 
1 
2 
3 
4 
3 
2 
1 
0 
1 
2 
5 
4 
3 
2 
1 
0 
1 
6 
5 
4 
3 
2 
1 
0 
Figure 1: Two-way Table showing all possible differences. 
Probabilities depend on the rules of the game. Merging simple events such as tossing two 
dice and noting the difference generally results in a much more complex sample space than the 
initial event. A single fair die has equiprobable outcomes. On the other hand, in the case of the 
difference of two fair dice, the outcomes are not equally likely. One reason for the lack of 
understanding of the dice difference game lies in the equiprobability bias (Lecoutre, 1992), 
which describes one’s tendency to view the probability of random events as being equal because 
“it reflects a process by chance”. Therefore, equiprobability bias occurs because people 
heuristically determine the chance of an event by simply considering the number of possible 
cases. In the game, this means that the probability of winning is calculated by dividing the 
number of possible outcomes (i.e., three) by the number of alternatives (i.e., six), which leads to 
the flawed judgment that the game is fair. These findings resonate with findings discussed in 
literature. 

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Australian Journal of Teacher Education 
Vol 45, 5, May 2020 
99