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Questions and Answers
What is the classical method in probability?
What is the classical method in probability?
Define an event in probability.
Define an event in probability.
Set of outcomes from a sample space
What is an experiment in the context of probability?
What is an experiment in the context of probability?
Activity for which the outcome is uncertain
What does the law of large numbers state?
What does the law of large numbers state?
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What is the law of total probability?
What is the law of total probability?
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What is the outcome of an experiment?
What is the outcome of an experiment?
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What does P(A) represent?
What does P(A) represent?
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What is a probability model?
What is a probability model?
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Define a tree diagram.
Define a tree diagram.
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What is the relative frequency method?
What is the relative frequency method?
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Is the empirical method the same as the relative frequency method?
Is the empirical method the same as the relative frequency method?
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What is a sample space in probability?
What is a sample space in probability?
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Subjective probability is based on personal judgment.
Subjective probability is based on personal judgment.
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Mutually exclusive events can occur at the same time.
Mutually exclusive events can occur at the same time.
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What does the term disjoint refer to in probability?
What does the term disjoint refer to in probability?
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What is the complement of event A?
What is the complement of event A?
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Define intersection of A and B.
Define intersection of A and B.
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What does the union of A and B mean?
What does the union of A and B mean?
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State the addition rule for A and B.
State the addition rule for A and B.
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What is the conditional probability of B given A?
What is the conditional probability of B given A?
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What characterizes independent events A and B?
What characterizes independent events A and B?
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What is the multiplication rule for independent events A and B?
What is the multiplication rule for independent events A and B?
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State the multiplication rule for dependent events A and B.
State the multiplication rule for dependent events A and B.
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What does the 1% rule refer to?
What does the 1% rule refer to?
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Sampling with replacement means an item can be selected only one time.
Sampling with replacement means an item can be selected only one time.
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In sampling without replacement, items can be selected more than once.
In sampling without replacement, items can be selected more than once.
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Define a combination in probability.
Define a combination in probability.
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What is a permutation?
What is a permutation?
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What is the factorial of a number n?
What is the factorial of a number n?
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What does the multiplication rule for counting state?
What does the multiplication rule for counting state?
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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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Description
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.
