Algebra Probability Flashcards

Questions and Answers

What is an outcome?

A possible result of an experiment.

What is an event?

A specific outcome, or collection of outcomes.

What is a sample space?

The set of all possible outcomes.

What is theoretical probability?

When all events are equally likely. Signup and view all the answers

What does p(a) refer to?

The probability of Event A. Signup and view all the answers

What is experimental probability?

Probability based on data collected over repeated trials. Signup and view all the answers

What are odds in favor?

A comparison between good results and bad results. Signup and view all the answers

What are odds against?

A comparison between bad results and good results. Signup and view all the answers

What are compound events?

Combines two or more events using the words 'and' or 'or'. Signup and view all the answers

What are mutually exclusive events?

Two events that have no overlapping outcomes. Signup and view all the answers

What are overlapping events?

Two events that have one or more outcomes in common. Signup and view all the answers

What does P(a or b) represent?

The probability of Event A or Event B. Signup and view all the answers

What does P(a & b) represent?

The probability of Event A and Event B. Signup and view all the answers

What are independent events?

Two events in which the first has no effect on the outcome of the second (replacement). Signup and view all the answers

What are dependent events?

Two events in which the first outcome does affect the outcome of the second (non-replacement). Signup and view all the answers

What are perfect squares?

Numbers that are the result of squaring another number (1, 4, 9, 16, 25, etc.). Signup and view all the answers

What are prime numbers?

Numbers that can only be divided by 1 and themselves (2, 3, 5, 7, 11, 13, 17, etc.). Signup and view all the answers

What is a multiple of a number?

The result of multiplying a number by any other number. Signup and view all the answers

What is a factor of a number?

Any number that divides evenly into another number. Signup and view all the answers

How do you find the sample space for an event?

Create a tree diagram, then list the possible results. Signup and view all the answers

What is the difference between experimental probability and theoretical probability?

Experimental probability is based on actual outcomes, while theoretical probability is based on equal likelihood for all outcomes. Signup and view all the answers

What is the difference between probability and odds?

Probability describes likelihood, while odds compare good results to bad results. Signup and view all the answers

What numerical values are possible for probability?

Only numbers from 0 to 1. Signup and view all the answers

How do you find an AND probability for independent events (with replacement)?

Find the probability of the first event and multiply it by the probability of the second event. Signup and view all the answers

How do you find an AND probability for a dependent event (without replacement)?

Find the probability of the first event, then multiply it by the probability of the second event. Signup and view all the answers

How do you find an OR probability for mutually exclusive events?

Find the probability of the first event and add it to the probability of the second event. Signup and view all the answers

How do you find an OR probability for overlapping events?

Find the probability of the first event, add the probability of the second event, but subtract the probability of being an outcome in both events. Signup and view all the answers

What do you need to find the experimental probability of an event?

Data from trials or conducting the experiment yourself and knowing the number of trials. Signup and view all the answers

What does it mean to compare experimental and theoretical probability?

Determine if experimental probability is less, more, or equal compared to theoretical probability. Signup and view all the answers

How do you reduce a fraction?

Find the largest number that can go into both the numerator and the denominator and divide them both. Signup and view all the answers

Study Notes

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.

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Description

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.