Q: Which of the following is the correct formula for theoretical probability?

$$P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}$$

Question 1

Which of the following best describes the difference between theoretical and empirical probability?

Accepted Answer

Theoretical probability is calculated before an experiment using possible outcomes, while empirical probability is calculated after an experiment using observed outcomes.

Question 2

If you roll a fair six-sided die, what is the theoretical probability of rolling a number greater than 4?

Accepted Answer

$$\frac{2}{6}$$

Question 3

A coin is tossed 100 times and lands on heads 56 times. What is the empirical probability of getting heads?

Accepted Answer

$$\frac{56}{100}$$

Question 4

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

Accepted Answer

$$\frac{3}{6}$$

Question 5

A bag contains 3 quarters, 4 nickels, 6 dimes, and 7 pennies. If you pick a coin at random, what is the probability that it is a dime?

Accepted Answer

$$\frac{6}{20}$$

Question 6

In a survey, Group 1 has 68 people wearing jeans and 43 not wearing jeans. What is the probability that a randomly selected person from Group 1 is not wearing jeans?

Accepted Answer

$$\frac{43}{111}$$

Question 7

Which of the following is the correct formula for theoretical probability?

Accepted Answer

$$P(	ext{event}) = \frac{	ext{number of favorable outcomes}}{	ext{total number of possible outcomes}}$$

Question 8

If the probability of an event is $$0.25$$, what is the probability that the event does NOT occur?

Accepted Answer

$$0.75$$

Question 9

A coin is flipped three times. What is the sample space for this experiment?

Accepted Answer

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

Question 10

If you roll two six-sided dice, what is the probability that the sum is 7?

Accepted Answer

$$\frac{6}{36}$$

Question 11

Which of the following statements about probability is TRUE?

Accepted Answer

The probability of any event is always between 0 and 1, inclusive.

Question 12

A student flips a coin 20 times and gets 8 heads. What is the empirical probability of getting heads?

Accepted Answer

$$\frac{8}{20}$$

Question 13

If the sample space for an experiment is $$S = \{a, b, c, d\}$$, what is the probability of randomly selecting 'b'?

Accepted Answer

$$\frac{1}{4}$$

Question 14

A box contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, what is the probability that it is not blue?

Accepted Answer

$$\frac{7}{10}$$

Question 15

Which of the following is an example of a sample space for flipping two coins?

Accepted Answer

$$\{HH, HT, TH, TT\}$$

Question 16

If you have a bag with 4 red marbles and 6 blue marbles, and you pick one at random, what is the probability it is red?

Accepted Answer

$$\frac{4}{10}$$

Question 17

A student claims that the probability of rolling a 7 on a standard six-sided die is $$\frac{1}{6}. Is $$this correct?

Accepted Answer

No, because 7 is not a possible outcome on a six-sided die.

Question 18

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

Accepted Answer

$$1$$

Question 19

A coin is flipped and a die is rolled. What is the probability of getting heads and a 6?

Accepted Answer

$$\frac{1}{12}$$

Question 20

Which of the following best describes a sample space?

Accepted Answer

A list of all possible outcomes of an experiment.

Basic Concepts of Probability: Theoretical and Empirical Approaches

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