$$P(A) = \dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$

$$P(A) = \dfrac{\text{Number of ways event A can occur}}{\text{Total number of possible outcomes}}$$

Question 1

Which of the following best describes a 'simple event' in probability theory?

Accepted Answer

An event that cannot be broken down into smaller events and consists of a single outcome.

Question 2

Given a single coin flip, what is the sample space $$S$$?

Accepted Answer

$$S = \{H, T\}$$

Question 3

If you flip three coins, which of the following represents the full event sample space?

Accepted Answer

$$\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$$

Question 4

What is the probability $$P(A) of an $$event $$A$$ occurring, according to the classical definition?

Accepted Answer

$$P(A) = \dfrac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}}$$

Question 5

Which of the following statements about probability is TRUE?

Accepted Answer

Probability is expressed as a decimal or a fraction between 0 and 1.

Question 6

If the probability of an event $$A is$$ $$P(A) = 0$$, what does this mean?

Accepted Answer

The event $$A is $$impossible.

Question 7

Which of the following is an example of a classical probability scenario?

Accepted Answer

Rolling a fair six-sided die and calculating the chance of getting a 4.

Question 8

Suppose you flip a coin twice. What is the probability of getting exactly one head?

Accepted Answer

$$\dfrac{1}{2}$$

Question 9

Which of the following best describes relative (frequency) probability?

Accepted Answer

Probability determined by observing the event over many trials in the real world.

Question 10

A medical researcher observes that out of 200 patients, 50 recover after a new treatment. What is the relative probability of recovery?

Accepted Answer

$$P = \dfrac{50}{200} = 0.25$$

Question 11

Which of the following is NOT a type of probability measure discussed in the notes?

Accepted Answer

Absolute Probability

Question 12

If an event is guaranteed to happen, what is its probability?

Accepted Answer

$$P = 1$$

Question 13

A student rolls a fair six-sided die. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\dfrac{2}{6} = \dfrac{1}{3}$$

Question 14

Which of the following best describes the general form of probability for an event $$A$$?

Accepted Answer

$$P(A) = \dfrac{	ext{Number of ways event A can occur}}{	ext{Total number of possible outcomes}}$$

Question 15

In a game, the probability of winning is $$0.2. $$What is the probability of not winning?

Accepted Answer

$$0.8$$

Question 16

Which of the following is a correct statement about the range of probability values?

Accepted Answer

$$0 \leq P(A) \leq 1$$

Question 17

A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability that it is blue?

Accepted Answer

$$\dfrac{3}{8}$$

Question 18

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

Accepted Answer

Estimating the likelihood of rain tomorrow based on personal judgment.

Question 19

If you flip a coin three times, what is the probability of getting exactly two heads?

Accepted Answer

$$\dfrac{3}{8}$$

Question 20

Which of the following best describes the concept of a sample space?

Accepted Answer

The set of all possible outcomes of an experiment.

Introduction to Probability in Statistics

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