Probability Fundamentals: How to Calculate Chances

Probability measures how likely an event is to occur, expressed as a number from 0 (impossible) to 1 (certain). Despite sounding abstract, probability governs everyday decisions — from weather forecasts to insurance premiums to the odds of a medical test being correct.

Basic probability formula

P(event) = number of favorable outcomes / total possible outcomes. Rolling a 4 on a fair die: P = 1/6 ≈ 0.167, or about 16.7%. Drawing a heart from a shuffled deck: P = 13/52 = 1/4 = 25%. These assume each outcome is equally likely.

The addition and multiplication rules

For mutually exclusive events (cannot both happen): P(A or B) = P(A) + P(B). For independent events (one does not affect the other): P(A and B) = P(A) × P(B). Rolling two dice and getting two sixes: P = 1/6 × 1/6 = 1/36 ≈ 2.8%.

Conditional probability

P(A | B) — the probability of A given B has occurred — equals P(A and B) / P(B). This is the basis of Bayes' theorem, which underpins spam filters, medical diagnostics, and predictive text. If a medical test is 95% accurate for a disease that affects 1% of people, a positive test does not mean a 95% chance of being sick — conditional probability explains why.