Calculate probabilities of events

Learning Objectives Define and calculate the theoretical probability of a single event. Calculate the probability of the complement of an event using the complement rule. Distinguish between mutually exclusive and non-mutually exclusive events and apply the appropriate Addition Rule to calculate their probabilities. Distinguish between independent and dependent events and apply the appropriate Multiplication Rule. Calculate conditional probabilities using the formula P(A|B) = P(A and B) / P(B). Interpret and solve complex probability problems involving combined events from word problems or data tables. What are the chances your favorite team wins the championship, or that you'll ace your next test? 🏆 Probability is the mathematics of chance! This tutorial will move be...

TermDefinitionExample Sample Space (S)The set of all possible outcomes of a random experiment.When rolling a standard six-sided die, the sample space is S = {1, 2, 3, 4, 5, 6}. Event (E)A specific outcome or a set of outcomes from the sample space.When rolling a die, the event 'rolling an even number' is the set E = {2, 4, 6}. Complement of an Event (E')The set of all outcomes in the sample space that are not in event E. It represents the event E not happening.If the event is 'rolling a 6' (E = {6}), the complement is 'not rolling a 6' (E' = {1, 2, 3, 4, 5}). Mutually Exclusive EventsTwo or more events that cannot occur at the same time. They have no outcomes in common.When drawing one card from a deck, the events 'drawing a King' and &#03...

The Complement Rule P(A') = 1 - P(A) The probability that an event A will not occur is 1 minus the probability that it will occur. This is useful for calculating the probability of 'at least one' of something happening. The Addition Rule for Probability P(A \cup B) = P(A) + P(B) - P(A \cap B) Calculates the probability that event A OR event B (or both) will occur. If the events are mutually exclusive, P(A \cap B) = 0, and the formula simplifies to P(A \cup B) = P(A) + P(B). The Multiplication Rule for Independent Events P(A \cap B) = P(A) \times P(B) Calculates the probability that two independent events, A AND B, will both occur. To use this, you must confirm the events are independent. The Conditional Probability Formula P(A|B) = \frac{P(A \cap...