Algebra Probability Flashcards

Probability Terminology

• Outcome: A possible result of an experiment, crucial for defining what can happen.
• Event: Refers to a specific outcome or a collection of outcomes from an experiment.
• Sample Space: The complete set of all possible outcomes for a probability experiment.
• Theoretical Probability: Assumes all outcomes are equally likely, calculating the likelihood based on this uniformity.
• Experimental Probability: Derives from actual data accrued over repeated trials, reflecting real-world outcomes.

Probability Notation

• P(A): Represents the probability of Event A occurring; a foundational concept in probability theory.
• P(A or B): The probability that event A or event B occurs.
• P(A and B): The probability that both event A and event B occur simultaneously.

Odds Definitions

• Odds in Favor: The ratio comparing favorable results to unfavorable results.
• Odds Against: The ratio comparing unfavorable results to favorable results.

Event Relationships

• Compound Events: Formed by combining multiple events using "and" or "or".
• Mutually Exclusive Events: Two events that cannot happen at the same time, having no overlapping outcomes.
• Overlapping Events: Events that share one or more outcomes.

Types of Events

• Independent Events: Events where the outcome of one does not affect the other, typically with replacement.
• Dependent Events: Events where the outcome of one influences the outcome of another, typically without replacement.

Special Number Definitions

• Perfect Squares: Numbers resulting from squaring integers (e.g., 1, 4, 9, 16, 25).
• Prime Numbers: Numbers greater than 1, divisible only by 1 and themselves (e.g., 2, 3, 5, 7).
• Multiples of a Number: Results from multiplying the number by any integer (e.g., multiples of 3 include 3, 6, 9).
• Factors of a Number: Numbers that divide evenly into another number (e.g., factors of 20 are 1, 2, 4, 5, 10, 20).

Probability Calculation Techniques

• Finding Sample Space: Use a tree diagram to visualize and list all potential outcomes.
• Independent Events (AND Probability): Multiply the probabilities of each event and simplify.
• Dependent Events (AND Probability): Calculate the probability of the first event and multiply by the adjusted probability of the second event.
• Mutually Exclusive OR Probability: Add the probabilities of both events directly.
• Overlapping Events OR Probability: Add the probabilities of both events and subtract the joint probability.

Comparisons and Assessments

• Experimental vs. Theoretical Probability: Compare the calculated likelihood of an event to the actual trial outcomes to see discrepancies.
• Range of Probability Values: Probabilities are always between 0 (impossible) and 1 (certain).

Fraction Management

• Reducing a Fraction: Identify the greatest common divisor of the numerator and denominator and divide by this number to simplify.

Explore key terms and concepts in probability through these flashcards. Each card defines essential vocabulary relating to outcomes, events, and probability types, making it an excellent study tool for mastering algebraic probability. Perfect for students looking to enhance their understanding of this important mathematical topic.