Defining Probability
Probability is a numerical measure representing the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Often, it's also represented as a percentage between 0% and 100%.
Key Principles and Calculation
The basic principle for calculating the probability of a specific event is to divide the number of favorable outcomes by the total number of all possible outcomes. This assumes all outcomes are equally likely. Key terms include 'experiment' (the process), 'outcome' (a single result), 'event' (a collection of one or more outcomes), and 'sample space' (all possible outcomes).
A Practical Example: Rolling a Die
Consider rolling a standard six-sided die. The sample space consists of six possible outcomes: {1, 2, 3, 4, 5, 6}. If we want to find the probability of rolling an even number, the favorable outcomes are {2, 4, 6}, which is 3 outcomes. Therefore, the probability is 3 (favorable outcomes) / 6 (total outcomes) = 1/2 or 0.5.
Importance and Applications
Probability is fundamental to understanding randomness and making informed decisions in an uncertain world. It is widely applied across various fields, including science, engineering, finance, weather forecasting, sports analytics, and medicine, helping to predict trends, assess risks, and design experiments.