Problem 54 - College Algebra

Question

Describe the difference between theoretical probability and empirical probability.

Step-by-Step Solution

Answer

Theoretical probability relies on mathematical principles to predict outcomes, assuming each event has an equal chance of occurrence. Empirical probability, on other hand, is based on observations and experiments.

Step 1: Definition of Theoretical Probability

Theoretical Probability is a probability that is calculated using mathematical models when all outcomes are equally likely. It's determined by considering all possible outcomes logically. The formula is given by P(E) = Number of favorable outcomes / Total number of outcomes.

Step 2: Definition of Empirical Probability

Empirical Probability is a probability that is based on actual experiments and direct observations or experiences. This type of probability is determined by carrying out a series of experiments and counting those where the event occurred and where it did not. The formula is P(E) = Number of times the event occurs / Total number of trials

Step 3: Comparing Theoretical and Empirical Probability

The main difference between theoretical and empirical probability comes down to approach. Theoretical probability uses mathematical principles and assumptions, while empirical probability relies on actual experiments and observations. Theoretical probability doesn't require the event to occur for knowing the outcome, whilst empirical probability needs the event to take place in order to collect the data or conduct the experiment.