Q: A password consists of 3 letters (A–Z) followed by 2 digits (0–9), with no repeats allowed. How many different passwords are possible?

$$26 \times 25 \times 24 \times 10 \times 9$$

Question 1

A probability experiment consists of rolling a fair six-sided die and then flipping a fair coin. What is the total number of possible outcomes in the sample space for this experiment?

Accepted Answer

$$6 	imes 2 = 12$$

Question 2

A survey asks respondents to select their favorite fruit (apple, banana, orange) and their preferred drink (water, juice, soda). Using the Fundamental Counting Principle, how many different combinations of fruit and drink are possible?

Accepted Answer

$$3 	imes 3 = 9$$

Question 3

Which of the following is an example of empirical probability?

Accepted Answer

A survey finds that 120 out of 400 people prefer tea over coffee, so the probability is $$\frac{120}{400}.$$

Question 4

A four-digit security code uses the digits 0–9, and each digit can be repeated. What is the probability of randomly generating the code 1234?

Accepted Answer

$$\frac{1}{10^4$}$$

Question 5

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

Accepted Answer

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

Question 6

Which of the following statements best describes the law of large numbers?

Accepted Answer

As the number of trials increases, the empirical probability approaches the theoretical probability.

Question 7

A license plate consists of three letters (A–Z) followed by three digits (0–9). If letters and digits can be repeated, how many different license plates are possible?

Accepted Answer

$$26^3$$ 	imes $$10^3$$

Question 8

A standard deck of 52 playing cards is shuffled. What is the probability of drawing a heart?

Accepted Answer

$$\frac{13}{52}$$

Question 9

A probability is reported as $$-0.2. $$What does this indicate?

Accepted Answer

The probability is not valid because probabilities cannot be negative.

Question 10

A survey of 3000 social media users found that 765 were aged 25–34. What is the probability that a randomly selected user is not 25–34 years old?

Accepted Answer

$$1 - \frac{765}{3000} = \frac{2235}{3000}$$

Question 11

A weather forecaster says there is a 90% chance of rain tomorrow. This probability is best classified as:

Accepted Answer

Subjective probability

Question 12

A coin is tossed and a spinner numbered 1–8 is spun. What is the probability of tossing a tail and spinning an odd number?

Accepted Answer

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

Question 13

A college ID number consists of 8 digits (0–9), and each digit can be repeated. What is the probability of randomly generating your own ID number?

Accepted Answer

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

Question 14

Which of the following is a simple event?

Accepted Answer

Selecting a specific defective machine part from a batch

Question 15

A password consists of 3 letters (A–Z) followed by 2 digits (0–9), with no repeats allowed. How many different passwords are possible?

Accepted Answer

$$26 	imes 25 	imes 24 	imes 10 	imes 9$$

Question 16

If the probability of an event E is $$0.05$$, what is the probability of the complement of E?

Accepted Answer

$$1 - 0.05 = 0.95$$

Question 17

A medical researcher estimates the probability of a patient recovering from a new treatment as 0.7 based on previous clinical trials. This probability is:

Accepted Answer

Empirical probability

Question 18

A student randomly guesses on a multiple-choice question with 4 options. What is the classical probability that the student selects the correct answer?

Accepted Answer

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

Question 19

A company has 4 possible manufacturers, 2 car sizes, and 5 colors for a new car model. How many different car options are available?

Accepted Answer

$$4 	imes 2 	imes 5 = 40$$

Question 20

Which of the following probabilities represents an unusual event?

Accepted Answer

$$0.03$$

Basic Concepts of Probability and Counting

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