Answer: The probability of a possible event is always between 0 and 1, inclusive, where 0 indicates impossibility and 1 indicates certainty.
Probability is a measure of the likelihood or chance that a specific event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility, 1 indicates certainty, and values between 0 and 1 represent the degree of likelihood. In mathematical terms, if P(A) represents the probability of event A, then:
- P(A) = 0 means event A is impossible.
- P(A) = 1 means event A is certain.
- 0 < P(A) < 1 means event A is possible, with higher values indicating higher likelihood.
The probability of a possible event is determined based on various factors, observations, or information available. There are different approaches to calculating probability:
Classical Probability:
- Applies to situations where each possible outcome is equally likely.
- Formula: P(A) = Number of favorable outcomes / Total number of possible outcomes.
Empirical Probability:
- Based on observed data or past experiences.
- Formula: P(A) = Number of times A occurs / Total number of observations.
Understanding the context of the problem is crucial for choosing the appropriate method to calculate probability. Probability theory is widely used in various fields such as statistics, finance, physics, and machine learning to make informed predictions and decisions based on uncertain information.