Probability for Math Olympiad: Complete Preparation Guide

Probability is one of the most intuitive yet tricky topics in Math Olympiads. What makes it challenging is that our natural instincts about chance are often wrong — and Olympiad papers exploit this beautifully.

For Class 10 students, competition problems test your ability to define sample spaces correctly, calculate theoretical probabilities, work with complementary events, and solve multi-step probability puzzles.

Mistakes:

* Sample space errors — For two dice, there are 36 outcomes (not 12). (3,4) is different from (4,3).
* Probability range — $0 \leq P(E) \leq 1$. If your answer is outside this range, recheck.
* "At least one" problems — Use complement: $P(\text{at least one}) = 1 - P(\text{none})$.
* Playing cards — 52 cards, 4 suits (13 each), 12 face cards, 4 aces. Know these counts cold.

Try these!