Classical, empirical, or subjective probability. How is each calculated? What does each one mean?
- There's a 50% chance that the result of a coin flip will be heads. There's an 80% chance that the best basketball player on your team will make a free throw. There's a 75% chance that the unemployment rate in the United States will drop next year. Not only are these three probabilities about three very different events, these are also three different categories of probabilities. The coin flip is an example of classical probability.
The free throw example is an example of empirical probability. Both of these are objective probabilities, meaning they are based on calculations. The unemployment example is an example of subjective probability. Here, there are no calculations. So what's the difference between these three different types of probabilities, and when is each appropriate? Let's begin with the coin flip, an example of classical probability.
Assuming this is a fair coin, we have two possible outcomes, heads and tails, both equally as likely. Let's say you win the coin flip if heads is the result. What's the probability of victory? How do we calculate this probability? One outcome is a winner, and we divide it by two, the total number of outcomes. Your chance of winning is 50%. We could do this with dice also. We have a six-sided die, six possible outcomes.
You win if you roll a one or a two. Two winning outcomes divided by six possible outcomes. Your probability of winning here is 33%. As you can see, classical probability works well when you know all possible outcomes and all the possible outcomes are equally likely to occur. When things are fair and equal, when we understand every possible outcome, classical probability works well.
But what happens when not everything is fair and equal? For this, we turn to empirical probability. In this case, we're trying to understand the probability that a particular basketball player will get a free throw. To calculate this probability, we simply divide the number of free throws this player has made this season divided by the number of free throws they attempted. This is different from classical probability, because here each free throw is different.
Consider all the factors that go into each free throw. Player health, player fatigue, game situation, early in the game, late in the game, playoff game, home game or away game. Since every situation is different, we can only count on the observations we have made up to this point. Obviously, the more observations we have, the safer we feel about the validity of our calculated probability. Early in a season, you may want to rely on last season's free throw data.
In the playoffs, you may want to rely only on free throws made in pressure situations. Empirical probability is not perfect. But when you have some data for repeatable situations, sometimes empirical probability can give you a nice idea of what to expect. But what happens when reliable data just isn't available? How can we possibly know if the unemployment rate in the United States will drop next year? There are so many factors to consider.
And what happened last year, or 10 years ago, or even what's happened over the last 100 years, may not be a good indicator of what will happen next year. In the case of unemployment probability, people often use their opinions, their experiences, and perhaps some related data to influence their statements about probability. So yes, people sort of just guess. Some guesses might be better than others, though. An economist's opinion may be more valuable than a lawyer's opinion.
A CEO's opinion may be more valuable than a rock star's opinion. Next time you read a probability somewhere, consider what type of probability it is. Is it a classical probability, one that you know is fair and reliable? Is it an empirical probability, one that is based on past data? Or is it a subjective probability, simply an opinion-based probability based on someone's experience and knowledge? If you understand what type of probability you've been given, you can better understand how reliable it might be.
Professor Eddie Davila covers statistics basics, like calculating averages, medians, modes, and standard deviations. He shows how to use probability and distribution curves to inform decisions, and how to detect false positives and misleading data. Each concept is covered in simple language, with detailed examples that show how statistics are used in real-world scenarios from the worlds of business, sports, education, entertainment, and more. These techniques will help you understand your data, prove theories, and save time, money, and other valuable resources—all by understanding the numbers.
- Calculate mean and median for specific data sets.
- Explain how the mode is used to assess a data set.
- Identify situations in which standard deviation can be used to investigate individual data points.
- Use mean and standard deviation to find the Z-score for a data point.
- List the three different categories of probability.
- Analyze data to determine if two events are dependent or independent.
- Predict possible outcomes for a situation using basic permutation calculations.
- Give examples of binomial random variables.