Probability measures how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). Understanding probability helps with decision-making, risk assessment, and interpreting statistics in the news and daily life.

Simple probability is calculated as favorable outcomes divided by total possible outcomes. The probability of rolling a 3 on a fair die is 1/6, because there is 1 favorable outcome out of 6 possible outcomes. This foundational concept applies to coins, cards, spinners, and real-world situations.

Compound probability involves multiple events. The probability of flipping two heads in a row is 1/2 × 1/2 = 1/4. Students learn to distinguish between independent events (coin flips) and dependent events (drawing cards without replacement), which changes how probabilities combine.

Expected value calculates the average outcome over many trials. If you win $10 half the time and lose $6 half the time, the expected value is (0.5 × 10) + (0.5 × -6) = $2 per game. This concept is fundamental to statistics, insurance, and decision theory.