A recent study highlights ways for students to enhance their understanding and interpretation of conditional probabilities.
A fresh investigation from LMU reveals effective strategies for students to grasp and interpret conditional probabilities.
How reliable is a positive HIV test result? What are the chances of actually being infected if the test shows positive? Even professionals can struggle with these questions, which might result in incorrect diagnoses and unnecessary surgeries. A team of mathematics education researchers from the Universities of Regensburg, Kassel, Freiburg, Heidelberg University of Education, and LMU Munich have conducted a study with medical and law students, comparing four different training courses aimed at enhancing understanding of probabilities. The outcomes of this project, known as TrainBayes and funded by the German Research Foundation, are now published in the journal Learning and Instruction.
The research focused on Bayesian scenarios. For example, if at a certain stage during the COVID-19 pandemic, only 0.1% of the population was infected with SARS-CoV-2 and someone took a self-test, there’s a 96% chance that an infected individual would receive a positive test result. However, there’s also a 2% chance that a healthy person could get a positive result. What does this imply? How probable is it that the individual is indeed infected upon receiving a positive test result?
“Many individuals — including specialists in their fields — tend to overestimate this probability significantly,” points out LMU mathematics educator Karin Binder, a co-author of the study. “The positive indicators of the tests lead people to place undue trust in the results while ignoring the minuscule percentage of actual infections.”
To clarify this scenario, imagine testing 100,000 people. Only about 100 are infected, yielding 96 positive results. Meanwhile, among the 99,900 healthy individuals, 2% (or 1,998) also test positive. Thus, out of 2,094 total positive test results, only 96 correspond to actual infections—roughly 5%. Therefore, a positive test result alone should not trigger alarm.
Lead author Nicole Steib from the University of Regensburg explains, “Converting probabilities (2%) into concrete numbers (1,998 out of 99,900) and representing this with a double tree structure helped students most effectively tackle similar problems.” In contrast, the typical probability trees used in classrooms are more beneficial for those with strong prior mathematical skills. The next phase of this project aims to incorporate these new training methods into school curricula.
