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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

When a certain type of thumbtack is tossed, the probability that it lands tip up is \(60 \%\), and the probability that it lands tip down is \(40 \%\). All possible outcomes when two thumbtacks are tossed are listed. U means the tip is Up, and D means the tip is Down. \(\begin{array}{llll}\mathrm{UU} & \mathrm{UD} & \mathrm{DU} & \mathrm{DD}\end{array}\) a. What is the probability of getting exactly one Down? b. What is the probability of getting two Downs?

Imagine rolling a fair six-sided die three times. a. What is the theoretical probability that all three rolls of the die show a 1 on top? b. What is the theoretical probability that the first roll of the die shows a 6 AND the next two rolls both show a 1 on the top.

A true/false test has 20 questions. Each question has two choices (true or false), and only one choice is correct. Which of the following methods is a valid simulation of a student who guesses randomly on each question. Explain. (Note: there might be more than one valid method.) a. Twenty digits are selected using a row from a random number table. Each digit represents one question on the test. If the number is even the answer is correct. If the number is odd, the answer is incorrect. b. A die is rolled 20 times. Each roll represents one question on the test. If the die lands on a 6 , the answer is correct; otherwise the answer is incorrect. c. A die is rolled 20 times. Each roll represents one question on the test. If the die lands on an odd number, the answer is correct. If the die lands on an even number, the answer is incorrect.

For each of the values, state whether the number could be the probability of an event. Give a reason for your answers. a. \(0.26\) b. \(-0.26\) c. \(2.6\) d. \(2.6 \%\) e. 26

A jury is supposed to represent the population. We wish to perform a simulation to determine an empirical probability that a jury of 12 people has 5 or fewer women. Assume that about \(50 \%\) of the population is female, so the probability that a person who is chosen for the jury is a woman is \(50 \%\). Using a random number table, we decide that each digit will represent a juror. The digits 0 through 5 , we decide, will represent a female chosen, and 6 through 9 will represent a male. Why this is a bad choice for this simulation?
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