Definition

Noun: - The probability of two events occurring together: This is a fundamental concept in probability theory. It quantifies the likelihood that two specific events, often labeled A and B, will both happen at the same time or in the same trial. It is denoted as P(A and B) or P(A ∩ B).

Usage

The term is used primarily in statistical, mathematical, and scientific contexts to describe the intersection of events. - It is a core component for calculating other important probabilities, such as conditional probability. - The joint probability of two independent events is the product of their individual probabilities: P(A and B) = P(A) * P(B).

Examples

Advanced Usage

• Joint Probability Distribution: This extends the concept to multiple random variables, describing the probability that each variable falls within a specific range or set of values simultaneously.
  • The joint probability distribution of height and weight was analyzed for the population sample.

Variants and Related Words

• Joint Distribution (n): A function that gives the joint probability for every possible combination of values for a set of random variables.
• Marginal Probability (n): The probability of a single event occurring, derived from a joint distribution by summing (or integrating) over all possibilities of the other events.
• Conditional Probability (n): The probability of one event occurring given that another event has already occurred, calculated as P(A|B) = P(A and B) / P(B).

Synonyms

• Concurrent probability (less common)
• Probability of intersection

Related Concepts (Not Phrasal Verbs or Idioms)

• Independence: Two events are independent if the occurrence of one does not affect the probability of the other. For independent events, P(A and B) = P(A) * P(B).
• Dependence: If events are not independent, their joint probability must be calculated differently, often using conditional probability: P(A and B) = P(A|B) * P(B).

Noun

1. the probability of two events occurring together