Probability — Single and Compound Events

GRE Quantitative · Axiom Academy

LESSON Probability — Single and Compound Events One event, two events, and the rule that tells you whether to multiply or add — including how "without replacement" quietly changes the second draw. 1. A Single Event Is a Fraction of Outcomes Every probability question starts the same way: count the outcomes you'd accept ( favorable ), count every outcome that could happen ( total ), and divide. Watch six equally-likely die faces light up one at a time — the running fraction on the right is exactly favorable ÷ total as each face is checked against "is it a 3?" The complement rule — every outcome is either the event or "not the event" 2. Compound AND: Multiply Along the Branches When two events must both occur, a tree diagram makes the rule visual: draw a branch for the first event's outcomes, then from the end of each branch, draw the second event's outcomes. The probability of any full path is just the product of the numbers along it — that's where "P(A and B) = P(A) × P(B)" comes from. Without replacement (dependent): the pool shrinks, so P(2nd) is conditioned on the 1st With replacement (independent): the marble goes back, so P(2nd) never changes

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