Elementary Statistics: Picturing the World (6th Edition)

Published by Pearson
ISBN 10: 0-32191-121-0
ISBN 13: 978-0-32191-121-6

Chapter 3 - Probability - Section 3.1 Basic Concepts of Probability and Counting - Exercises: 5

Answer

As an experiment is repeated over and over, the empirical probability of an event approaches the theoretical (actual) probability of the event.

Work Step by Step

The Law of Large Numbers can be described as such: As you increase the number of times a probability experiment is repeated, the empirical probability (relative frequency) of an event approaches the theoretical (actual) probability of the event. As an example of this law, suppose you want to determine the probability of tossing a head with a fair coin. If you toss the coin 10 times and get only 3 heads, you obtain an empirical probability of $\frac{3}{10}$. Because you tossed the coin only a few times, your empirical probability is not representative of the theoretical probability, which is $\frac{1}{2}$. If, however, you toss the coin several thousand times, then the law of large numbers tells you that the empirical probability will be very close to the theoretical or actual probability.
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