What is Probability?
Probability measures how likely an event is to happen, expressed as a number between 0 and 1. It underlies everything from dice games and card draws to weather forecasts and risk assessment.
Probability is calculated as P(A) = n(A)/n(S) — the number of favorable outcomes divided by the total number of possible outcomes. It always falls between 0 (impossible) and 1 (certain).
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Step-by-step worked examples
Rolling a fair six-sided die, what is the probability of rolling a 4?
n(A) = 1 (only one face shows 4) n(S) = 6 (six faces total) P(4) = 1/6 ≈ 0.167
What is the probability of drawing a red card from a standard 52-card deck?
n(A) = 26 red cards n(S) = 52 total cards P(red) = 26/52 = 0.5
What is the probability of drawing an ace or a king from a deck?
n(ace) = 4, n(king) = 4, total = 52 P(ace) = 4/52, P(king) = 4/52 P(ace or king) = 8/52 = 2/13 ≈ 0.154
Flashcards
Quick quiz
Q1.A fair coin is flipped. What is P(heads)?
Q2.A bag has 4 red and 6 blue balls. What is P(red)?
Q3.Which value CANNOT be a probability?
Q4.If P(A) = 0.3, what is P(not A)?
The full card deck, worked steps and AI-tutor support for “What is Probability?” are in Notek — study by hand before your exam.
Common mistakes
Thinking probability can exceed 1. — Correct: Probability is always between 0 and 1 inclusive.
Adding probabilities of non-exclusive events without adjustment. — Correct: Use P(A or B) = P(A) + P(B) − P(A and B) when events overlap.
Confusing odds with probability. — Correct: Odds compare favorable to unfavorable outcomes; probability compares favorable to total.
Assuming past outcomes affect independent future ones (gambler's fallacy). — Correct: Independent events have the same probability every time, regardless of history.
FAQ
What is probability?
Probability is a measure between 0 and 1 of how likely an event is to occur, calculated as favorable outcomes divided by total outcomes.
What is the formula for probability?
P(A) = n(A)/n(S), where n(A) is favorable outcomes and n(S) is total possible outcomes.
How do you calculate probability with examples?
Divide the number of favorable outcomes by total outcomes — e.g., rolling a die, P(4) = 1/6.
What are some real probability examples?
Coin flips, dice rolls, card draws, weather forecasts, and lottery odds are all common examples.