Basic Probability — SAT Math Explained
The mathematical study of likelihood. The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes: P(event) = favorable outcomes / total outcomes.
The Core Idea
Probability quantifies uncertainty on a scale from 0 (impossible) to 1 (certain). It's expressed as a fraction, decimal, or percentage and represents long-run frequency — how often something happens over many trials.
Key Vocabulary
A process with an uncertain outcome
The set of all possible outcomes
A specific outcome or set of outcomes you're interested in
Outcomes that satisfy the event condition
Calculated from known information — assumes equally likely outcomes
Observed from actual trials — (successes / total trials)
Probability Scale
Impossible — cannot happen
Equally likely to happen or not
Certain — always happens
Unlikely
Likely
Complement Rule
P(event not happening) = 1 - P(event). If P(rain) = 0.3, then P(no rain) = 0.7
Real World Applications
Rolling a die: P(rolling a 4) = 1/6
Drawing a card: P(drawing a heart) = 13/52 = 1/4
Weather forecasting: 70% chance of rain
Quality control: probability that a manufactured item is defective
Common Errors to Avoid
Writing probability greater than 1 (impossible — probabilities are always ≤ 1)
Counting outcomes that don't satisfy the event in the numerator
Confusing theoretical and experimental probability
Practice: Basic Probability
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A fair six-sided die is rolled once. What is P(rolling a 4)?
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