6.1 Three Types of Probability

What is the probability of rolling a 1 on a six-sided die? How do you know this? How can you justify that number?

There are three types of probability.

1. Empirical Probability: If you could repeat a random process over and over again, you’d get a sense of the possible outcomes and their associated probabilities by calculating their relative frequency in the long run. If you repeatedly tossed a balanced die, then the relative frequency of 1’s after tossing the die MANY times would be the empirical probability. If you repeatedly got a sample of 100 people, the relative frequency of estimated odds ratios below 1 would be the empirical probability of getting an odds ratio below 1.

2. Theoretical Probability: If you don’t have time to toss a die a million times, you could calculate probabilities based on mathematical theory and assumptions. When tossing a balanced die, you would assume that each side is equally likely to land face-up. Thus the chance of rolling a 1, is 1/6 for a six-sided die.

What is the probability that you’ll talk to someone you do not know this week? What does that number represent? How can you justify that number?

3. Subjective Probability: If you use a number between 0 and 1 (100%) to reflect your uncertainty in an outcome (rather than based on empirical evidence or mathematical theory), then you are using subjective probability.

In this class, we’ll focus on theoretical and empirical probability. In particular, we will use computational tools to estimate empirical probabilities using simulations (such as bootstrapping and randomization tests) and mathematical tools to estimate theoretical probabilities.