$$\text{Expected heads} = 100 \times 0.5 = 50$$

Question 1

Which of the following best describes the difference between an outcome and an event in probability theory?

Accepted Answer

An outcome is a single result of an experiment, while an event is any subset of outcomes, possibly including more than one.

Question 2

A fair die is rolled once. What is the probability that the number rolled is greater than 4?

Accepted Answer

$$P = \frac{2}{6} = 0.3333$$

Question 3

In a classroom of 35 students, 19 are male. If one student is chosen at random, what is the probability that the student is female?

Accepted Answer

$$P = \frac{16}{35} = 0.4571$$

Question 4

Which of the following statements about probability is TRUE?

Accepted Answer

A probability must always be between 0 and 1, inclusive.

Question 5

If the probability of rain tomorrow is 0.20, which of the following is the correct notation?

Accepted Answer

$$P(R) = 0.20$$

Question 6

A fair coin is tossed 100 times. According to the frequentist interpretation, what is the expected number of heads?

Accepted Answer

$$	ext{Expected heads} = 100 	imes 0.5 = 50$$

Question 7

Which of the following best describes the sample space for rolling two fair dice and summing the spots?

Accepted Answer

The sample space is the set of all possible sums from 2 to 12.

Question 8

If an event has a probability of 0, what does this mean?

Accepted Answer

The event is impossible.

Question 9

A fair die is rolled. What is the probability of rolling an even number?

Accepted Answer

$$P = \frac{3}{6} = 0.5000$$

Question 10

Which formula is used to calculate the probability of an event when all outcomes are equally likely?

Accepted Answer

$$P = \frac{f}{N}$$

Question 11

In the context of probability, what does the term 'sample space' refer to?

Accepted Answer

The set of all possible outcomes of an experiment.

Question 12

A two-pack-a-day smoker has a probability of 0.75 of dying from cancer. According to the frequentist interpretation, what does this mean?

Accepted Answer

If many two-pack-a-day smokers are observed, about 75% will die from cancer.

Question 13

If you roll two fair dice, which sum is most likely to occur?

Accepted Answer

7

Question 14

Which of the following is NOT a valid probability value?

Accepted Answer

1.5

Question 15

A fair die is rolled. What is the probability of rolling a number less than 3?

Accepted Answer

$$P = \frac{2}{6} = 0.3333$$

Question 16

If you toss a fair coin 1600 times, which outcome would most likely indicate the coin is NOT fair?

Accepted Answer

1000 heads

Question 17

Which of the following best illustrates the concept of relative frequency in probability?

Accepted Answer

The proportion of times an event occurs in repeated trials of an experiment.

Question 18

A fair die is rolled. What is the probability of rolling a 5?

Accepted Answer

$$P = \frac{1}{6} = 0.1667$$

Question 19

Which of the following is an example of an event that consists of more than one outcome?

Accepted Answer

Rolling an even number on a fair die.

Question 20

If the probability of an event is 1, what does this mean?

Accepted Answer

The event is certain to occur.

Introduction to Probability in Statistics

Study Guide - Practice Questions