Q: A car security system access code consists of 4 digits (0-9). If each digit can be used only once and not repeated, how many different access codes are possible?

$$10 \times 9 \times 8 \times 7 = 5040$$

Q: A car's access code consists of 4 digits (0-9). If each digit can be repeated, but the first digit cannot be 0 or 1, how many codes are possible?

$$8 \times 10 \times 10 \times 10 = 8000$$

Question 1

A university assigns student ID numbers using 8 digits, where each digit can be any number from 0 to 9 and digits can be repeated. What is the probability that a randomly generated 8-digit number matches your student ID number?

Accepted Answer

$$\frac{1}{10^8$}$$

Question 2

A car security system access code consists of 4 digits (0-9). If each digit can be used only once and not repeated, how many different access codes are possible?

Accepted Answer

$$10 	imes 9 	imes 8 	imes 7 = 5040$$

Question 3

You roll a fair six-sided die. What is the probability of rolling a number less than 5?

Accepted Answer

$$\frac{4}{6} = \frac{2}{3}$$

Question 4

A probability experiment consists of tossing a coin and spinning a spinner numbered 1 through 8. What is the probability of tossing a tail and spinning an odd number?

Accepted Answer

$$\frac{4}{16} = \frac{1}{4}$$

Question 5

A survey of 3000 social media users found that 765 were aged 25 to 34. What is the empirical probability that the next user surveyed is 25 to 34 years old?

Accepted Answer

$$\frac{765}{3000} = 0.255$$

Question 6

Which of the following best describes subjective probability?

Accepted Answer

A probability based on intuition, educated guesses, or estimates.

Question 7

If the probability of an event $$E is$$ $$0.3$$, what is the probability of the complement of $$E$$?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 8

A company offers 3 manufacturers, 2 car sizes, and 4 colors for a new car. How many different ways can you select one manufacturer, one car size, and one color?

Accepted Answer

$$3 	imes 2 	imes 4 = 24$$

Question 9

Which of the following is an example of classical probability?

Accepted Answer

The probability of winning a 1000-ticket raffle with one ticket is $$\frac{1}{1000}.$$

Question 10

Which statement best describes the Law of Large Numbers?

Accepted Answer

As an experiment is repeated, the empirical probability approaches the theoretical probability.

Question 11

A probability experiment consists of rolling a die and flipping a coin. How many outcomes are in the sample space?

Accepted Answer

$$6 	imes 2 = 12$$

Question 12

If an event consists of rolling a 4, 5, or 6 on a six-sided die, is this a simple event?

Accepted Answer

No, because it consists of more than one outcome.

Question 13

A car's access code consists of 4 digits (0-9). If each digit can be repeated, but the first digit cannot be 0 or 1, how many codes are possible?

Accepted Answer

$$8 	imes 10 	imes 10 	imes 10 = 8000$$

Question 14

Which of the following is NOT a property of probability?

Accepted Answer

The probability of an event can be negative.

Question 15

A survey finds that 560 out of 1502 adults read only print books last year. What is the empirical probability that a randomly selected adult read only print books?

Accepted Answer

$$\frac{560}{1502}$$

Question 16

Which of the following best describes a simple event?

Accepted Answer

An event that consists of a single outcome.

Fundamental Counting Principle and Basic Probability Concepts

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