Let’s start with a simple question,
How do you know something is likely to happen?
Do you go with gut feeling? Past experience? Or calculate it on paper?
The way we measure and assign probability depends on the situation. That’s why statisticians developed multiple Approaches to Probability each designed for different kinds of uncertainty.
In this article, we’ll walk through the three core approaches: Classical, Empirical, and Subjective. Each has its own logic, formula (if any), and use-case. Let’s break them down.
Classical (A Priori) Probability
This is the oldest and most straightforward method. It assumes all outcomes are equally likely.
Formula:
P(E) = Number of favorable outcomes / Total number of possible outcomes
Example: The probability of getting a 4 when rolling a fair die = 1/6
Characteristics:
- Requires a well-defined sample space
- Applies to symmetric and controlled experiments (coins, dice, cards)
- Doesn’t require actual experiments relies on theoretical logic
Limitations:
- Not applicable to real-life situations where outcomes aren’t equally likely
- Fails when past data or frequencies are more reliable than assumptions
Empirical (Frequentist) Probability
Here, probability is based on observation not theory.
Formula:
P(E) = Number of times event E occurs / Total number of trials
Example: A machine failed 4 times in 100 days. So, empirical probability of failure = 4/100 = 0.04
Characteristics:
- Relies on actual experiments or historical data
- More realistic for business, finance, quality control, etc.
- Accuracy increases with larger sample size
Limitations:
- Requires a large number of trials to stabilize probability estimates
- Cannot be used in hypothetical or rare scenarios (e.g., nuclear disasters)
Subjective Probability
This is where intuition, experience, and judgment come into play. No formulas — just human reasoning.
Example: A stock analyst says there's a 70% chance the market will rise tomorrow based on news, sentiment, and patterns.
Characteristics:
- Depends on the individual’s belief or expertise
- Used in business strategy, legal decisions, forecasting, sports predictions
- Flexible when data is unavailable
Limitations:
- Subjective, may be biased or inconsistent
- Hard to verify or test accuracy
Quick Flick
| Aspect | Classical | Empirical | Subjective |
|---|---|---|---|
| Basis | Assumption (equal likelihood) | Past data or observation | Opinion or belief |
| Formula | Yes | Yes | No |
| Use-case | Games, dice, cards | Business, manufacturing | Forecasting, strategy |
| Objectivity | High | Moderate | Low |
| Accuracy improves with data? | No | Yes | Depends |
Examples
- Classical: Probability of drawing a king from a standard deck = 4/52
- Empirical: Based on last 100 product shipments, 3 arrived late → Probability = 3/100 = 0.03
- Subjective: A CEO estimates a 60% chance of launching the product next quarter
Summary
- Probability isn’t one-size-fits-all. The context determines the approach.
- Use Classical when outcomes are equally likely and defined.
- Use Empirical when you have enough past data.
- Use Subjective when data is scarce and expert judgment matters.
That’s how statisticians handle uncertainty with precision — or at least, with informed guesses.
Next time you say, "I think there's a 50% chance this will happen," ask yourself, Am I guessing? Or do I have data or logic to back it up?
The beauty of probability lies in better questions. Mastering its approaches helps you ask them smarter.