Probabilities of compound events

Learning Objectives Define compound events, independent events, dependent events, mutually exclusive events, and inclusive events. Differentiate between independent and dependent events in a given scenario. Distinguish between mutually exclusive and inclusive events. Calculate the probability of two independent events occurring using the multiplication rule. Calculate the probability of two dependent events occurring. Calculate the probability of 'A or B' for both mutually exclusive and inclusive events using the appropriate addition rules. Solve word problems involving compound events by selecting and applying the correct formula. What are the chances of you rolling doubles in a board game AND your opponent landing on your property? 🎲 Let's find out! This...

TermDefinitionExample Compound EventAn event that consists of two or more simple events. These events can be linked with words like 'and' or 'or'.Rolling a 4 on a die AND flipping a tail on a coin. Independent EventsTwo events where the outcome of one event does not affect the probability or outcome of the other event.Flipping a coin twice. The result of the first flip has no impact on the result of the second flip. Dependent EventsTwo events where the outcome of the first event changes the probability of the second event.Drawing a card from a deck, NOT replacing it, and then drawing a second card. The first draw changes the cards available for the second draw. Mutually Exclusive EventsTwo events that cannot happen at the same time. They have no outcomes in common.When...

Multiplication Rule for Independent Events P(A \text{ and } B) = P(A) \times P(B) Use this rule when you want to find the probability of two independent events both happening. You multiply their individual probabilities. Multiplication Rule for Dependent Events P(A \text{ and } B) = P(A) \times P(B|A) Use this for dependent events. P(B|A) means 'the probability of B happening, given that A has already happened'. The probability of the second event is adjusted based on the first event's outcome. Addition Rule for Mutually Exclusive Events P(A \text{ or } B) = P(A) + P(B) Use this when you want to find the probability of one event OR another mutually exclusive event happening. You simply add their probabilities. General Addition Rule for Inclusive Ev...