Welcome to understanding probability! Probability is a mathematical way to measure how likely something is to happen. It's expressed as a number between 0 and 1, where 0 means impossible and 1 means certain. For example, a fair coin flip has a probability of 0.5 or 50% for landing on heads.
Theoretical probability is used when all outcomes are equally likely. The formula is simple: divide the number of favorable outcomes by the total number of possible outcomes. For example, when rolling a standard six-sided die, the probability of getting an odd number is 3 out of 6, which equals one-half or 50 percent.
Empirical probability is based on actual observations and experiments. Instead of theoretical calculations, we collect data and count how often an event occurs. For example, if we flip a coin 100 times and get heads 51 times, the empirical probability of heads is 51 out of 100, or 0.51. This approach is useful when theoretical probability is difficult to calculate.
Subjective probability relies on personal judgment when data is limited or unavailable. This includes expert opinions, past experience, and intuition. For example, a meteorologist might estimate a 30% chance of rain based on weather patterns, or an investor might believe there's a 60% chance the stock market will rise. While less precise than mathematical calculations, subjective probability is valuable for unique or future events.
To summarize, there are three main methods to determine probability. Use theoretical probability when outcomes are equally likely, empirical probability when you have observational data, and subjective probability when relying on expert judgment. These methods have wide applications in weather forecasting, medical diagnosis, financial analysis, quality control, and risk assessment. Understanding probability helps us make better decisions in uncertain situations.