Moh Hasbi Assidiqi

A Survey of Probability Concepts


Understanding probability is crucial for making informed decisions in uncertain situations. This article delves into various probability concepts, providing a comprehensive overview.

Probability is a numerical measure of the likelihood that a particular event will occur, expressed as a number between 00 and 11. An experiment is a process that leads to one of several possible outcomes, and an event is a collection of one or more outcomes from an experiment. Each possible result of an experiment is known as an outcome.

Classical probability is based on the assumption of equally likely outcomes. For example, the probability of drawing a king from a standard deck of cards is calculated as 452=0.0769\frac{4}{52} = 0.0769, meaning there is about a 7.69%7.69\% chance of drawing a king.

Empirical probability, on the other hand, is based on observed data. For instance, if 6565 out of 100100 students prefer online learning, the empirical probability is 65100=0.65\frac{65}{100} = 0.65. This indicates a 65%65\% chance that a student prefers online learning.

Subjective probability is based on personal judgment rather than objective data. It reflects an individual’s degree of belief in the occurrence of an event, making it more personal and less quantifiable.

The addition rule of probability helps calculate the probability of either of two events occurring. For example, if the probability that a tourist visits Site A is 0.60.6 and Site B is 0.50.5, and the probability of visiting both is 0.30.3, then the probability of visiting at least one site is

P(A or B)=P(A)+P(B)−P(A and B)=0.6+0.5−0.3=0.8P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) = 0.6 + 0.5 - 0.3 = 0.8

Thus, there is an 80%80\% chance that the tourist visits at least one site.

The complement rule calculates the probability of an event not occurring. For example, if the probability of visiting Site A is 0.70.7, the probability of not visiting Site A is

P(not A)=1−P(A)=1−0.7=0.3P(\text{not } A) = 1 - P(A) = 1 - 0.7 = 0.3

This means there is a 30%30\% chance that the person does not visit Site A.

By understanding these fundamental concepts, you can better analyze and interpret various probabilistic scenarios, enhancing your decision-making skills in uncertain environments.

Concepts: Probability, Experiment, Event, Outcome, Classical probability, Empirical probability, Subjective probability, Addition rule of probability, Complement rule

References: