What method of assigning probabilities to a simple event uses relative frequencies?

Verified step by step guidance

1. Understand that in probability theory, there are different methods to assign probabilities to events, such as classical, subjective, and empirical methods.
2. Recognize that the method which uses relative frequencies is called the empirical or frequentist method of assigning probabilities.
3. Recall that relative frequency is calculated by dividing the number of times an event occurs by the total number of trials or observations.
4. Express the probability of an event \(E\) using relative frequency as \(P(E) = \frac{\text{Number of times } E \text{ occurs}}{\text{Total number of trials}}\).
5. Conclude that this method bases the probability on observed data rather than theoretical assumptions.

Key Concepts

Relative Frequency

Relative frequency is the ratio of the number of times an event occurs to the total number of trials or observations. It is used to estimate the probability of an event based on empirical data from experiments or observations.

Empirical Probability

Empirical probability assigns probabilities to events based on observed data rather than theoretical reasoning. It relies on relative frequencies obtained from actual experiments or historical data to estimate the likelihood of an event.

Simple Event

A simple event is an outcome or result that cannot be broken down further in a probability experiment. Understanding what constitutes a simple event is essential for correctly applying relative frequencies to assign probabilities.