Algebra 2 · AP Statistics

Probability

Favorable outcomes, independent events, and the "or" rule.

The idea

The probability of an event is the fraction of outcomes that count as a "win," out of every equally likely outcome:

P(event) = favorable outcomes / total outcomes

When two events are independent (one doesn't affect the other), multiply their probabilities to find the chance both happen:

P(A and B) = P(A) × P(B)

To find the chance that either of two events happens, add their probabilities — then subtract the overlap, so you don't double-count outcomes that satisfy both:

P(A or B) = P(A) + P(B) − P(A and B)

Practice problems

Problem 1

A fair six-sided die is rolled once. What's the probability of rolling an even number?

Show answer

3 favorable outcomes (2, 4, 6) out of 6: P = 3/6 = 1/2.

Problem 2

A bag contains 5 red marbles and 7 blue marbles. One marble is drawn at random. Find P(red).

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P(red) = 5 / (5 + 7) = 5/12.

Problem 3

Two fair coins are flipped. Find the probability that both land on heads.

Show answer

The flips are independent: P = (1/2) × (1/2) = 1/4.

Problem 4

A card is drawn from a standard 52-card deck. Find the probability it's a king or a heart.

Show answer

P(king) = 4/52, P(heart) = 13/52, P(king and heart) = 1/52 (the king of hearts). P(king or heart) = 4/52 + 13/52 − 1/52 = 16/52 = 4/13.