Statistics Chapter 5 Flashcards

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?

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

What is the law of total probability?

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

What is the outcome of an experiment?

Result of a single trial of an experiment Signup and view all the answers

What does P(A) represent?

Probability of event A Signup and view all the answers

What is a probability model?

Table that represents a situation and follows all the rules of probability Signup and view all the answers

Define a tree diagram.

A diagram with branches each representing a possible outcome Signup and view all the answers

What is the relative frequency method?

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

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

Yes Signup and view all the answers

What is a sample space in probability?

Collection of all possible outcomes; S Signup and view all the answers

Subjective probability is based on personal judgment.

True Signup and view all the answers

Mutually exclusive events can occur at the same time.

False Signup and view all the answers

What does the term disjoint refer to in probability?

Mutually exclusive Signup and view all the answers

What is the complement of event A?

"NOT"; all outcomes in the sample space that are not in event A Signup and view all the answers

Define intersection of A and B.

"AND"; all outcomes that belong to both A and B Signup and view all the answers

What does the union of A and B mean?

"OR"; all outcomes that belong to A or B Signup and view all the answers

State the addition rule for A and B.

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

What is the conditional probability of B given A?

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

What characterizes independent events A and B?

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

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

P(A) x P(B) Signup and view all the answers

State the multiplication rule for dependent events A and B.

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

What does the 1% rule refer to?

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

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

False Signup and view all the answers

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

False Signup and view all the answers

Define a combination in probability.

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

What is a permutation?

n choices; r selections; no repetition; order important Signup and view all the answers

What is the factorial of a number n?

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

What does the multiplication rule for counting state?

Total number of different outcomes for multiple events; no order; repetition or no repetition 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.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

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.