Podcast
Questions and Answers
Classical probability is a measure of the likelihood of an ______ occurring.
Classical probability is a measure of the likelihood of an ______ occurring.
event
The classical probability of an event A is denoted by ______ and is calculated as:
The classical probability of an event A is denoted by ______ and is calculated as:
P(A)
The set of all possible outcomes of an experiment is called the ______ space.
The set of all possible outcomes of an experiment is called the ______ space.
Sample
The number of outcomes in the event set is referred to as the ______ outcomes.
The number of outcomes in the event set is referred to as the ______ outcomes.
Signup and view all the answers
The property that states 0 ≤ P(A) ≤ 1 is called ______.
The property that states 0 ≤ P(A) ≤ 1 is called ______.
Signup and view all the answers
The probability of the sample space is equal to ______, where S is the sample space.
The probability of the sample space is equal to ______, where S is the sample space.
Signup and view all the answers
Study Notes
Classical Probability
Definition
- Classical probability is a measure of the likelihood of an event occurring, based on the number of favorable outcomes and the total number of possible outcomes.
- It is also known as "a priori probability" or "theoretical probability".
Formula
- The classical probability of an event A is denoted by P(A) and is calculated as:
P(A) = Number of favorable outcomes / Total number of possible outcomes
Key Concepts
- Sample Space: The set of all possible outcomes of an experiment.
- Event: A set of one or more outcomes of an experiment.
- Favorable Outcomes: The number of outcomes in the event set.
- Total Number of Possible Outcomes: The total number of outcomes in the sample space.
Properties
- Non-Negativity: 0 ≤ P(A) ≤ 1
- Normalization: P(S) = 1, where S is the sample space
- Additivity: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A and B are events
Examples
- Rolling a fair six-sided die:
- Sample space: {1, 2, 3, 4, 5, 6}
- Event: rolling an even number
- Favorable outcomes: {2, 4, 6}
- P(even) = 3/6 = 1/2
- Drawing a card from a standard deck of 52 cards:
- Sample space: {52 possible cards}
- Event: drawing a heart
- Favorable outcomes: {13 hearts}
- P(heart) = 13/52 = 1/4
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of classical probability, including its definition, formula, and key concepts such as sample space, event, favorable outcomes, and total number of possible outcomes. Practice problems with rolling a die and drawing a card from a deck are also provided.
