A probability is a numerical measure of the chance that a particular event will occur.

A probability can range from 0.0 (impossible) to 1.0 (a sure thing). A probability of 0.5 is as likely as unlikely. How does one assign probabilities to experimental outcomes?

The classical method uses mathematical models to estimate probability.

Usually, finite sets with a countable number of elements are used.

What is the probability that you get a 2 or a 3 on one roll of a six-sided die? Using counting of discrete events,

The percent operator is a postfix "divide by 100.0" operator.

Thus, 50% is the same as 0.5.

In the empirical method, sometimes called the relative frequency method, the past is used as an indicator of the future probability.

In a course, 15 of 60 students earned a letter grade of A . What is the probability of getting a letter grade of A in the course?

Using relative frequency, the probability is

Of course, your mileage may vary.

What does that mean? It means that the probability that you get a letter grade of A in the course is 25.0% given that the only information available is that you are taking the course.

If other information is available (e.g., poor test scores, low cumulative GPA, etc.), that information might change the probability estimate.

A probability estimate is always dependent on the information upon which the estimate is based.

Consider the probability that a coin will land heads is 0.5 (and tails is 0.5) and that the coin has landed heads 5 (or 50) times in a row. What is the probability that the next flip will be heads?

The gambler's fallacy is to use relative frequency when a classical method is appropriate. For example, suppose that a coin has landed heads 5 (or 50) times in a row.

Under the classical method, the probability that it will land heads next time is still 0.5. Each flip is assumed to be independent of the other flips.

The subjective method uses the judgment of an expert to estimate the probability.

What is an expert?

Microsoft question, in attempting to determine the level of expertise of a user: Do you give more advice than you receive?

If a football team has won the last 8 of the last 10 games that it has played, what is the probability that it wins the next game.

What is the probability using the classical model?

Using the classical model, the probability is

What is the probability using the relative frequency model? Using the classical model, the probability is

What is the probability using the subjective model? Using the subjective model, the probability depends on the judgment of an expert.

Of course, additional information would change the probabilities.

• Classical statistics - abstract logic
• Empirical statistics - history, relative frequency
• Subjective statistics - opinion