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Chapter 5: Problem 3

A Monopoly player claims that the probability of getting a 4 when rolling a six-sided die is \(1 / 6\) because the die is equally likely to land on any of the six sides. Is this an example of an empirical probability or a theoretical probability? Explain.

Short Answer

Expert verified
This is an example of a theoretical probability because the player's conclusion is based not on repeated experiments or collected data, but on the logical assumption that each face of the die is equally likely to land up in a single throw.

Step by step solution

01

Understand Theoretical Probability

Theoretical Probability is the type of probability that we use when each outcome in a sample space is equally likely. It is derived purely from reasoning and logical analysis. Given a single roll of a six-sided die and asked to determine the probability of rolling a 4, each of the six outcomes (1, 2, 3, 4, 5, and 6) is equally likely. So, the probability is calculated as the number of ways that 4 can occur divided by the total number of outcomes. There is only one way to roll a 4, and there are six possible outcomes, so the theoretical probability of rolling a 4 is \(1/6\).
02

Understand Empirical Probability

Empirical probability is based on actual experiments and adequate recordings of the happening of events. This type of probability is based on the direct observations or experiences. The number of times an event happened is divided by the number of times the process was repeated. In the given scenario, the monopoly player didn't throw the dice many times and based his claim on the outcomes, hence it is not empirical probability.
03

Apply the Definitions to the Scenario

Now, applying these principles to the given scenario, it's clear that the Monopoly player鈥檚 reasoning refers to theoretical probability. The player isn't basing his statement on several dice throws, but on a logical analysis of what should happen when a six-sided die is thrown. Each of the six outcomes is equally likely in theory, regardless of what might happen in a particular run of throws. Hence, this is a theoretical probability.

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Most popular questions from this chapter

Some estimates say that \(10 \%\) of the population is left-handed. We wish to design a simulation to find an empirical probability that if five babies are born on a single day, one or more will be left-handed. Suppose we decide that the even digits \((0,2,4,\), 6,8 ) will represent left-handed babies and the odd digits will represent right-handed babies. Explain what is wrong with the stated simulation method, and provide a correct method.

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