Probability and Basic Counting

ACT Math · Axiom Academy

LESSON Probability and Basic Counting Favorable over total, AND versus OR, and the counting shortcuts that turn a slow list into one multiplication. 1. Basic Probability — Favorable Over Total Probability measures how likely an event is. Every outcome in the situation is equally likely, so you just count how many of them count as a "win" and divide by how many outcomes there are in total. the only formula you need for basic probability A standard die is rolled. What's the probability of rolling a 3 ? Favorable outcomes: 1 (just the 3 ). Total outcomes: 6 (faces 1 – 6 ). A deck has 52 cards, 4 of which are aces. What's the probability of drawing an ace? Favorable: 4 aces. Total: 52 cards. 2. Compound Probability — AND Multiplies, OR Adds When a question links two events together, the connecting word tells you the operation: AND means both events happen, so you multiply ; OR means at least one happens, so you add — then subtract any outcome you'd otherwise count twice. AND: multiply (if the events are independent) OR: add, then subtract the overlap A die is rolled twice. What's the probability of rolling two 3 s? Worked example — OR (with overlap) A card is drawn from a standard deck. What's the probability it's a king or a heart? , — but the king of hearts is counted in both, so subtract it once: . 3. The Counting Principle — Multiply the Choices

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