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 (B)

    What is a simulation?

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

    What is the sample space S?

    <p>The set of all possible outcomes.</p> Signup and view all the answers

    Define a probability model.

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

    What is an event in probability?

    <p>A collection of outcomes. (B)</p> Signup and view all the answers

    Mutually exclusive events can occur at the same time.

    <p>False (B)</p> Signup and view all the answers

    What does P(A^C) represent?

    <p>Probability of NOT A within the sample space.</p> Signup and view all the answers

    What is the complement rule in probability?

    <p>P(A^C) = 1 - P(A)</p> Signup and view all the answers

    State the addition rule for mutually exclusive events.

    <p>P(A or B) = P(A) + P(B)</p> Signup and view all the answers

    What is conditional probability?

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

    Describe the general multiplication rule.

    <p>P(A and B) = P(A ∩ B) = P(A) * P(B|A)</p> Signup and view all the answers

    Independent events change the probability of each other occurring.

    <p>False (B)</p> Signup and view all the answers

    What is the multiplication rule for independent events?

    <p>P(A ∩ B) = P(A) * P(B)</p> Signup and view all the answers

    State the general addition rule.

    <p>P(A or B) = P(A) + P(B) - P(A and B)</p> Signup and view all the answers

    What does the symbol ∪ represent?

    <p>Union (means 'or').</p> Signup and view all the answers

    What does the symbol ∩ signify?

    <p>Intersection (means 'and').</p> 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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    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!

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