AP Statistics Chapter 5 Review Flashcards

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Questions and Answers

What is the definition of probability?

The predicted outcome of an event.

A number between 0 and 1 that describes the proportion of times an outcome would occur. (correct)

The average result of multiple trials.

A fixed outcome in a given chance process.

What does the law of large numbers state?

Rare events will never happen.

All events are independent of each other.

The proportion of times a specific outcome occurs approaches a single value as repetitions increase. (correct)

Outcomes will always balance in a short series of trials.

The law of averages states that getting heads on a coin flip six times must be followed by getting tails six times.

False

What is a simulation?

An imitation of chance behavior based on a model. Signup and view all the answers

What is the sample space S?

The set of all possible outcomes. Signup and view all the answers

Define a probability model.

A description of a chance process consisting of a sample space and probabilities for each outcome. Signup and view all the answers

What is an event in probability?

A collection of outcomes. Signup and view all the answers

Mutually exclusive events can occur at the same time.

False Signup and view all the answers

What does P(A^C) represent?

Probability of NOT A within the sample space. Signup and view all the answers

What is the complement rule in probability?

P(A^C) = 1 - P(A) Signup and view all the answers

State the addition rule for mutually exclusive events.

P(A or B) = P(A) + P(B) Signup and view all the answers

What is conditional probability?

The probability that one event happens given that another event has occurred. Signup and view all the answers

Describe the general multiplication rule.

P(A and B) = P(A ∩ B) = P(A) * P(B|A) Signup and view all the answers

Independent events change the probability of each other occurring.

False Signup and view all the answers

What is the multiplication rule for independent events?

P(A ∩ B) = P(A) * P(B) Signup and view all the answers

State the general addition rule.

P(A or B) = P(A) + P(B) - P(A and B) Signup and view all the answers

What does the symbol ∪ represent?

Union (means 'or'). Signup and view all the answers

What does the symbol ∩ signify?

Intersection (means 'and'). Signup and view all the answers

Study Notes

Probability Concepts and Definitions

Probability is quantified between 0 and 1, representing the likelihood of an outcome occurring after numerous repetitions.
Law of Large Numbers states that as the number of trials increases, the empirical probability of an outcome converges to the expected probability.
Law of Averages is a common misconception that past outcomes influence future results; it wrongly suggests outcomes must balance out (e.g., after a string of heads, tails must follow).

Simulation Process

Simulation immitates chance events via a defined process:
- State: Formulate a question regarding a probability scenario.
- Plan: Outline the method to simulate a single trial.
- Do: Conduct multiple trials of the simulation.
- Conclude: Interpret findings to address the original question.

Key Probability Terms

Sample Space (S) encompasses all potential outcomes of a probability experiment.
Probability Model combines a sample space and probabilities assigned to each outcome.
Event refers to a specific subset of outcomes from the sample space, typically labeled with capital letters (e.g., A, B, C).

Event Relationships

Mutually Exclusive Events are those that cannot occur simultaneously; mathematically described as P(A and B) = 0.
Complement of A (P(A^C)) indicates the probability of event A not occurring.
Complement Rule simplifies finding P(A^C) as 1 - P(A).

Probability Rules

Addition Rule for Mutually Exclusive Events: For disjoint events A and B, P(A or B) can be calculated as P(A) + P(B).
Conditional Probability (P(B|A)) measures the likelihood of event B happening, given that event A has already occurred.

Multiplication Rules

General Multiplication Rule: Calculates the probability of both A and B occurring as P(A and B) = P(A) * P(B|A).
Independent Events do not affect each other's probabilities; therefore, P(A|B) equals P(A) and vice versa.
Multiplication Rule for Independent Events states that P(A and B) = P(A) * P(B).

Advanced Probability Rules

General Addition Rule: For overlapping events A and B, the formula is P(A or B) = P(A) + P(B) - P(A and B).

Symbols in Probability

The symbol ∪ denotes the union of two sets, indicating "or."
The symbol ∩ denotes the intersection of two sets, indicating "and."

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Description

Test your understanding of key concepts in probability with these flashcards from Chapter 5 of AP Statistics. Learn essential terms like 'probability' and the 'law of large numbers' through concise definitions. Perfect for quick reviews before exams!