math

Probability

Measures how likely something is to happen.

Formula for Probability

P(Event) = Number of favorable outcomes / Total number of possible outcomes

Complement Rule

The probability that an event does not happen.

Formula for Complement Rule

P(A') = 1 - P(A)

Addition Rule

Used for calculating the probability of at least one of two events occurring.

Formula for Addition Rule (overlapping events)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Formula for Addition Rule (mutually exclusive)

P(A ∪ B) = P(A) + P(B)

Multiplication Rule

Used for calculating the probability of two events occurring together.

Formula for Multiplication Rule (independent events)

P(A ∩ B) = P(A) × P(B)

Formula for Multiplication Rule (dependent events)

P(A ∩ B) = P(A | B) × P(B)

Conditional Probability

The probability that event A happens given that B already happened.

Formula for Conditional Probability

P(A | B) = P(A ∩ B) / P(B)

Independent Events

Events that do not affect each other.

Mutually Exclusive Events

Events that cannot happen together.

Venn Diagrams

Visual representations of sets and their relationships.

P(A ∪ B) formula

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A') formula

P(A') = 1 - P(A)

Key Phrase for 'A or B'

A ∪ B (Union) - Use the Addition Rule.

Key Phrase for 'A and B'

A ∩ B (Intersection) - Use the Multiplication Rule.

Key Phrase for 'A given B'

Conditional probability notation.

Complement of an Event

Not A is denoted as A'.

Final Tips for Solving Probability Problems

Draw diagrams, label work clearly, know formulas and keywords.