Which best describes probability?
Probability is a mathematical concept that describes the likelihood of an event
occurring. It is expressed as a number between 0 and 1, where 0 represents
an impossible event and 1 represents a certain event. A probability of 0.5, for
example, indicates an event has a 50% chance of occurring.
In statistics, probability is used to make predictions based on available data. It
allows us to make informed decisions by taking into account the likelihood of
different outcomes. Probability theory provides a framework for analyzing and
interpreting uncertain events, from simple coin tosses to complex systems in
science and engineering.
The foundations of probability theory were laid by mathematicians such as
Blaise Pascal and Pierre de Fermat in the seventeenth century. The
mathematical concept of probability has since been studied extensively and
applied in various fields such as science, economics, and engineering.
There are two main types of probability: theoretical probability and empirical
probability. Theoretical probability is based on mathematical models and
predictions, while empirical probability is derived from real-world observations
or experiments.
The study of probability has also given rise to probability distributions, which
describe the probabilities of different outcomes in a given system or process.
The most well-known probability distributions include the normal distribution,
the binomial distribution, and the Poisson distribution.
In summary, probability is a mathematical concept that describes the
likelihood of an event occurring. It is a crucial tool for making informed
decisions and making predictions based on available data. The concepts of
theoretical and empirical probability, as well as probability distributions, are
important in understanding probability theory and its applications.
References:
- Ross, S. M. (2003). Introduction to probability models. Academic press.
- Blitzstein, J. K., & Hwang, J. (2015). Introduction to probability. CRC press.
- Grinstead, C. M., & Snell, J. L. (2012). Introduction to probability (Vol. 71). American
Mathematical Soc.