6 Questions
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:
P(A)
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.
favorable
The property that states 0 ≤ P(A) ≤ 1 is called ______.
Non-Negativity
The probability of the sample space is equal to ______, where S is the sample space.
1
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
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.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
