Combined Events Probability — SAT Math Explained
The probability of two or more events occurring together (AND) or at least one of them occurring (OR), using the multiplication and addition rules respectively.
The Core Idea
When events are combined, the mathematics depends on whether they are independent (one doesn't affect the other) or dependent (one affects the probability of the other), and whether we want both or either.
Key Rules
P(A and B) = P(A) × P(B) — multiply probabilities
P(A and B) = P(A) × P(B|A) — multiply, but second probability changes
P(A or B) = P(A) + P(B) — add probabilities (can't both happen)
P(A or B) = P(A) + P(B) - P(A and B) — subtract overlap to avoid double-counting
P(not A) = 1 - P(A)
Independence Vs Dependence
Outcome of one event doesn't affect the other — rolling a die twice, flipping a coin after drawing a card WITH replacement
First event changes the sample space for the second — drawing cards WITHOUT replacement
With Vs Without Replacement
With replacement: probabilities stay constant (independent). Without replacement: probabilities change for each subsequent draw (dependent).
Common Errors to Avoid
Using the multiplication rule for OR events (that's for AND)
Forgetting to subtract the overlap in non-mutually-exclusive OR problems
Treating dependent events as independent when sampling without replacement
Practice: Combined Events Probability
5 SAT-style questions. Select your answer and get an instant explanation.
Two independent spins of a fair 4-section spinner (1–4). What is P(first is 2 AND second is 3)?
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