Probability
Overview
Probability measures how likely an event is, as a number from 0 (impossible) to 1 (certain). It is computed from the sample space — the set of all possible outcomes — by comparing the number of successful outcomes to the total. For compound events, independent probabilities multiply.
Vocabulary
- Probability
- The likeliness of an event occurring: P(event) = (number of favorable outcomes) ÷ (total number of equally likely outcomes).
- Sample Space
- The set of all possible outcomes of an experiment.
- Event
- An outcome, or set of outcomes, whose probability is being found.
- Independent Events
- Events in which the outcome of one does not affect the outcome of the other. For independent events, P(A and B) = P(A) · P(B).
- Without Replacement
- Drawing items and not returning them, so the total number of outcomes decreases for the next draw — the events are not independent.
Main Ideas
- P(5 on a die) = 1/6: one favorable side out of six equally likely outcomes.
- The probabilities of all outcomes in a sample space sum to 1.
- An impossible event has probability 0 — for example, P(7 on a standard die) = 0.
- Independent compound events: multiply. P(2 on a die and heads on a coin) = 1/6 × 1/2 = 1/12.
- Without replacement, adjust the counts before multiplying: P(two red in a row) from 26 red of 52 cards is 26/52 × 25/51.
- Always simplify the final fraction.
Lesson Notes
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Practice Problems
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