Probability of independent and dependent events

Learning Objectives Define independent and dependent events. Distinguish between independent and dependent events in various scenarios. Calculate the probability of two independent events occurring. Calculate the probability of two dependent events occurring. Apply probability concepts to solve real-world problems involving sequences of events. Ever wonder if flipping a coin twice means the first flip affects the second? 🪙 Or if drawing cards from a deck changes the chances for the next draw? 🤔 In this lesson, you'll learn how to figure out the chances of two things happening, whether one event changes the likelihood of the other or not. This skill helps you understand predictions and make better decisions in everyday situations, from games to scientific analysis. Rea...

TermDefinitionExample ProbabilityThe measure of the likelihood that an event will occur, expressed as a number between 0 and 1 (or 0% and 100%).The probability of flipping a coin and getting heads is 1/2. OutcomeA single possible result of an experiment or situation.When rolling a standard die, 'rolling a 3' is an outcome. EventA set of one or more outcomes from an experiment.When rolling a standard die, 'rolling an even number' is an event, consisting of outcomes {2, 4, 6}. Independent EventsTwo events are independent if the outcome of the first event does not affect the outcome or probability of the second event.Flipping a coin and getting heads, then rolling a die and getting a 6. The coin flip doesn't change the die roll's probability. Dependent EventsTwo...

Probability of Independent Events $P(A \text{ and } B) = P(A) \times P(B)$ To find the probability that two independent events, A and B, both occur, you multiply the probability of event A by the probability of event B. Probability of Dependent Events $P(A \text{ and } B) = P(A) \times P(B|A)$ To find the probability that two dependent events, A and B, both occur, you multiply the probability of event A by the probability of event B occurring GIVEN that event A has already occurred. $P(B|A)$ represents this conditional probability.