Statistics Chapter 5 Flashcards
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Questions and Answers

What is the classical method in probability?

  • Set of outcomes from a sample space
  • Number of outcomes in an event/Number of outcomes in a sample space (correct)
  • Activity for which the outcome is uncertain
  • Table that represents a situation and follows the rules of probability

    • Define an event in probability.

    Set of outcomes from a sample space

    What is an experiment in the context of probability?

    Activity for which the outcome is uncertain

    What does the law of large numbers state?

    <p>As the number of times an experiment is repeated grows, the relative frequency of an outcome approaches the probability of the outcome.</p> Signup and view all the answers

    What is the law of total probability?

    <p>Sum of all the outcome probabilities in a sample space equals 1</p> Signup and view all the answers

    What is the outcome of an experiment?

    <p>Result of a single trial of an experiment</p> Signup and view all the answers

    What does P(A) represent?

    <p>Probability of event A</p> Signup and view all the answers

    What is a probability model?

    <p>Table that represents a situation and follows all the rules of probability</p> Signup and view all the answers

    Define a tree diagram.

    <p>A diagram with branches each representing a possible outcome</p> Signup and view all the answers

    What is the relative frequency method?

    <p>Frequency of event/Number of trials of experiment</p> Signup and view all the answers

    Is the empirical method the same as the relative frequency method?

    <p>Yes</p> Signup and view all the answers

    What is a sample space in probability?

    <p>Collection of all possible outcomes; S</p> Signup and view all the answers

    Subjective probability is based on personal judgment.

    <p>True</p> Signup and view all the answers

    Mutually exclusive events can occur at the same time.

    <p>False</p> Signup and view all the answers

    What does the term disjoint refer to in probability?

    <p>Mutually exclusive</p> Signup and view all the answers

    What is the complement of event A?

    <p>&quot;NOT&quot;; all outcomes in the sample space that are not in event A</p> Signup and view all the answers

    Define intersection of A and B.

    <p>&quot;AND&quot;; all outcomes that belong to both A and B</p> Signup and view all the answers

    What does the union of A and B mean?

    <p>&quot;OR&quot;; all outcomes that belong to A or B</p> Signup and view all the answers

    State the addition rule for A and B.

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

    What is the conditional probability of B given A?

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

    What characterizes independent events A and B?

    <p>Occurrence of one event does not affect the probability that the other event will occur.</p> Signup and view all the answers

    What is the multiplication rule for independent events A and B?

    <p>P(A) x P(B)</p> Signup and view all the answers

    State the multiplication rule for dependent events A and B.

    <p>P(B/A) x P(A)</p> Signup and view all the answers

    What does the 1% rule refer to?

    <p>If the sample size is less than or equal to 1% of the population, assume successive draws from the population are independent.</p> Signup and view all the answers

    Sampling with replacement means an item can be selected only one time.

    <p>False</p> Signup and view all the answers

    In sampling without replacement, items can be selected more than once.

    <p>False</p> Signup and view all the answers

    Define a combination in probability.

    <p>n choices; r selections; no repetition; order not important</p> Signup and view all the answers

    What is a permutation?

    <p>n choices; r selections; no repetition; order important</p> Signup and view all the answers

    What is the factorial of a number n?

    <p>n!; n x (n-1) x (n-2) x (n-3) x...x 0</p> Signup and view all the answers

    What does the multiplication rule for counting state?

    <p>Total number of different outcomes for multiple events; no order; repetition or no repetition</p> Signup and view all the answers

    Study Notes

    Key Concepts in Probability and Statistics

    • Classical Method: Probability calculated as the ratio of the number of successful outcomes to the total number of outcomes in the sample space.
    • Event: A specific set of outcomes derived from the sample space.
    • Experiment: A defined activity where the result is uncertain.
    • Law of Large Numbers: As experiments are repeated, the observed frequency of outcomes will stabilize around their expected probabilities.
    • Law of Total Probability: The collective probabilities of all possible outcomes in a sample space equal one.
    • Outcome: The result from a single trial of an experiment.
    • Probability of Event A (P(A)): A numerical measure representing the likelihood of event A occurring.
    • Probability Model: A structured representation showing possible outcomes and their probabilities, ensuring each probability falls between 0 and 1, and sums to 1.
    • Tree Diagram: A visual representation used to depict all potential outcomes branching out from a starting point.
    • Relative Frequency Method: Probability determined by dividing the occurrence of an event by the number of trials.
    • Empirical Method: Another term for the relative frequency method; involves actual observed frequencies.
    • Sample Space (S): The complete set of all possible outcomes for an experiment.
    • Subjective Probability: Probability determined based on personal or subjective judgment rather than statistical analysis.
    • Mutually Exclusive Events: Two events that cannot occur simultaneously; their intersection probability is zero (P(A and B) = 0).
    • Disjoint: A synonym for mutually exclusive events.
    • Complement of A: Represents all outcomes in the sample space that are not part of event A.
    • Intersection of A and B: Outcomes that are shared by both events A and B; denoted as "AND".
    • Union of A and B: Outcomes included in either event A or B; denoted as "OR".
    • Addition Rule for A and B: Formula to find the probability of either event A or event B occurring, accounting for any overlap.
    • Conditional Probability of B given A (P(B/A)): Probability of event B occurring after confirming that event A has happened.
    • Independent Events: Two events where the occurrence of one does not affect the probability of the other.
    • Multiplication Rule for Independent Events: The joint probability of independent events A and B equals the product of their individual probabilities (P(A) x P(B)).
    • Multiplication Rule for Dependent Events: Takes into account the dependency of events; calculated as P(B/A) x P(A).
    • 1% Rule: When the sample size is ≤ 1% of the population, events are treated as independent during successive selections.
    • Sampling with Replacement: The same item can be chosen multiple times from the sample space.
    • Sampling without Replacement: An item can only be selected once from the sample space.
    • Combination: Choosing r selections from n options where order does not matter, and repetition is not allowed.
    • Permutation: Arranging r selections from n options where order is significant and without repetition.
    • Factorial (n!): The product of all positive integers up to n, representing the total arrangements possible.
    • Multiplication Rule for Counting: Used to determine the total number of different outcomes when combining multiple events.

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    Test your understanding of key concepts from Statistics Chapter 5 with these flashcards. Definitions include classical method, event, experiment, and the law of large numbers. Perfect for students looking to reinforce their comprehension of statistical principles.

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