Adolescent Reasoning on Probability Paradoxes: Cognitive Mechanisms Underlying Intuitive Success and Error

Varad Acharya, Harshit Mishra

Abstract: This study examined how 106 adolescents (ages 15?20, M=17.48, SD=1.67) approached three probability paradoxes: Monty Hall, Birthday Paradox, and Gambler's Fallacy. Performance varied dramatically across paradoxes, ?? (2, N=106) = 59.59, p<.001: Gambler's Fallacy (80.2% correct), Monty Hall (33.0%), and Birthday Paradox (6.6%). Advanced mathematics predicted Monty Hall success (OR=1.78) and especially Birthday Paradox success (OR=4.94). Female participants outperformed males on Gambler's Fallacy (OR=1.90), but had a reversed effect on Birthday Paradox (OR=0.5) an unexpected finding. Qualitative analysis of reasoning explanations identified systematic bias patterns: equiprobability thinking (Monty Hall), representativeness heuristic (Birthday), and sound independence reasoning (Gambler's Fallacy). Adolescents reported high confidence (M=7.84-8.27/10) despite 20-39% error rates, indicating severe metacognitive blindness on difficult tasks. These results demonstrate that adolescent probability reasoning is paradox-dependent: intuitive System 1 reasoning succeeds on independence tasks but fails catastrophically on conditional probability and combinatorics. Traditional instruction adequately teaches independence but neglects conditional probabilities and combinatorics misconceptions. Evidence-based interventions with explicit mechanism teaching, simulation-based learning, and confidence calibration training may bridge these gaps while preserving accurate intuitions on independence reasoning.

Keywords: probability paradoxes, adolescent cognition, conditional probability, Monty Hall Problem, cognitive biases, dual-process theory, mathematical reasoning

How to Cite?: Varad Acharya, Harshit Mishra, "Adolescent Reasoning on Probability Paradoxes: Cognitive Mechanisms Underlying Intuitive Success and Error", Volume 14 Issue 11, November 2025, International Journal of Science and Research (IJSR), Pages: 1535-1540, https://www.ijsr.net/getabstract.php?paperid=SR251120064734, DOI: https://dx.doi.org/10.21275/SR251120064734