Q: A four-digit access code uses digits 0-9, but each digit can be used only once. How many different codes are possible?

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

Question 1

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

Accepted Answer

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

Question 2

A company surveyed 1502 adults about their book reading habits. 560 read only print books, 108 read only digital books, 425 read both, and 409 read no books. What is the empirical probability that the next adult surveyed read only digital books?

Accepted Answer

$$\frac{108}{1502}$$

Question 3

Which of the following is an example of subjective probability?

Accepted Answer

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

Question 4

A college ID number consists of 8 digits, each from 0 to 9, and digits can be repeated. What is the probability of randomly generating your exact ID number?

Accepted Answer

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

Question 5

If the probability of an event E is 0.7, what is the probability of the complement of E?

Accepted Answer

$$0.3$$

Question 6

A die is rolled. What is the probability of rolling a number less than 5?

Accepted Answer

$$\frac{4}{6}$$

Question 7

A car’s security access code consists of 4 digits, each from 0 to 9. Digits can be repeated. How many different access codes are possible?

Accepted Answer

$$10^4$$

Question 8

Which of the following best describes the Law of Large Numbers?

Accepted Answer

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

Question 9

A survey of 3000 social media users found that 765 were aged 25 to 34. What is the probability that a randomly selected user is in this age group?

Accepted Answer

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

Question 10

If you select one manufacturer, one car size, and one color from the options: 3 manufacturers, 2 car sizes, and 4 colors, how many different car choices are possible?

Accepted Answer

$$3 	imes 2 	imes 4 = 24$$

Question 11

Which of the following statements is true about the range of probabilities rule?

Accepted Answer

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

Question 12

A simple event is best described as:

Accepted Answer

An event with only one outcome.

Question 13

If the probability of winning a 1000-ticket raffle with one ticket is $$\frac{1}{1000}$$, what type of probability is this?

Accepted Answer

Classical probability

Question 14

A quality inspector randomly selects a specific defective machine part from a batch. Is this a simple event?

Accepted Answer

Yes, because it consists of only one outcome.

Question 15

You roll a six-sided die. What is the probability of rolling a 7?

Accepted Answer

$$0$$

Question 16

Which of the following is NOT a valid sample space for tossing a coin?

Accepted Answer

{Heads, Tails, Edge}

Question 17

If an event E has a probability of 0, what does this mean?

Accepted Answer

The event is impossible.

Question 18

A four-digit access code uses digits 0-9, but each digit can be used only once. How many different codes are possible?

Accepted Answer

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

Question 19

Which of the following best describes empirical probability?

Accepted Answer

It is based on observed data from experiments.

Question 20

If the probability of an event is based on intuition or an educated guess, it is called:

Accepted Answer

Subjective probability

Chapter 3: Probability – Structured Study Notes for Statistics Students

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