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 codes are possible?

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

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 ID matches your own 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 codes are possible?

Accepted Answer

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

Question 3

Which of the following best describes empirical probability?

Accepted Answer

Probability based on observed data from experiments or surveys.

Question 4

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 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Which of the following is an example of subjective probability?

Accepted Answer

A doctor estimates a 90% chance of a patient’s full recovery based on experience.

Question 8

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 9

A company offers 3 manufacturers, 2 car sizes, and 4 colors for a new car. How many different car options are available?

Accepted Answer

$$3 	imes 2 	imes 4 = 24$$

Question 10

Which statement about the Law of Large Numbers is correct?

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

Which of the following is NOT a property of probability?

Accepted Answer

The probability of an event can be negative.

Question 13

A six-sided die is rolled. What is the probability of rolling a 7?

Accepted Answer

$$0$$

Question 14

A frequency distribution shows that 765 out of 3000 social media users are aged 25 to 34. What is the empirical probability that a randomly selected user is 25 to 34 years old?

Accepted Answer

$$\frac{765}{3000}$$

Question 15

If the probability of an event $$E is$$ $$0.25$$, which of the following statements is true?

Accepted Answer

The probability of the complement of $$E is$$ $$0.75.$$

Question 16

Which of the following is an example of classical probability?

Accepted Answer

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

Fundamental Counting Principle and Basic Probability Concepts

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