Question 1

Which of the following best describes a random process as illustrated by repeatedly rolling a fair die, as shown in the images above?

Accepted Answer

A process where the outcome of any particular roll is unknown, but the proportion of each outcome approaches a specific value as the number of rolls increases.

Question 2

Suppose you roll a fair six-sided die (as shown above) 600 times. According to the Law of Large Numbers, what is the expected proportion of times you will roll a '3'?

Accepted Answer

$$\frac{1}{6}$$

Question 3

If the sample space $$S$$ for rolling a single fair die is $$S = \{1, 2, 3, 4, 5, 6\}$$, what is the probability of rolling an even number?

Accepted Answer

$$\frac{1}{2}$$

Question 4

A loaded die is one in which certain outcomes are more likely than others. If a die is loaded so that rolling a '6' is twice as likely as any other number, what is the probability of rolling a '6'?

Accepted Answer

$$\frac{2}{7}$$

Question 5

Which of the following statements about probability models is TRUE?

Accepted Answer

Each probability in the model must be greater than or equal to 0 and less than or equal to 1.

Question 6

You roll a fair die 120 times and observe that the number '4' comes up 15 times. Using the empirical method, what is the probability of rolling a '4'?

Accepted Answer

$$\frac{1}{8}$$

Question 7

A fair die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 8

If you roll two fair dice, what is the probability that the sum of the numbers rolled is 7?

Accepted Answer

$$\frac{1}{6}$$

Question 9

Which of the following is an example of a subjective probability?

Accepted Answer

An economist estimates a 20% chance of recession next year based on their judgment.

Question 10

A probability experiment consists of rolling a single fair die. What is the sample space $$S$$ for this experiment?

Accepted Answer

$$S = \{1, 2, 3, 4, 5, 6\}$$

Question 11

Suppose you roll a fair die and want to find the probability of rolling a number less than 5. Using the classical method, what is this probability?

Accepted Answer

$$\frac{2}{3}$$

Question 12

If an event is impossible, what is its probability?

Accepted Answer

$$0$$

Question 13

A die is rolled 60 times and the number '2' appears 8 times. What is the empirical probability of rolling a '2'?

Accepted Answer

$$\frac{2}{15}$$

Question 14

Which of the following is NOT a requirement for a probability model?

Accepted Answer

Probabilities can be negative for rare events.

Question 15

If you roll a fair die, what is the probability of rolling either a 1 or a 6?

Accepted Answer

$$\frac{1}{3}$$

Question 16

A fair die is rolled. What is the probability of rolling a number that is both even and greater than 2?

Accepted Answer

$$\frac{1}{3}$$

Chapter 5: Probability – Foundations and Methods

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