Probability and Conditional Probability

SAT Math · Axiom Academy

Probability & Conditional Probability Master probability calculations and conditional probability from tables Probability measures how likely an event is to occur. It's expressed as a fraction, decimal, or percentage between 0 and 1. What is the probability of rolling a 3 on a standard six-sided die? Probability = 0 means the event is impossible Probability = 1 means the event is certain The sum of all possible outcomes' probabilities = 1 Compound Probability: "AND" & "OR" When combining events, we use specific rules depending on whether they're independent or mutually exclusive. Example 2: Probability of "AND" What is the probability of flipping heads AND rolling a 4? Example 3: Probability of "OR" What is the probability of rolling a 2 OR a 5 on a die? Conditional probability is the probability of an event occurring given that another event has already occurred. The key phrase is "given that" or "if." Example 4: Conditional Probability from Two-Way Table Survey of 100 students about sport preference: Question: Given that a student prefers basketball, what is the probability they are a boy? Independent vs. Dependent Events The type of event affects how you calculate probabilities. You have a bag with 5 red and 3 blue marbles. What's the probability of drawing two red marbles without replacement? Draw diagrams: Two-way tables, tree diagrams, and Venn diagrams help visualize probability Check independence: Ask if one event affects the other

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