Q: A company surveys 2000 people about their favorite fruit. 600 people choose apples. What is the empirical probability that a randomly selected person prefers apples?

$$ P(\text{apples}) = \frac{600}{2000} = 0.3 $$

Q: If a password consists of 3 letters followed by 2 digits (0-9), and letters and digits can be repeated, how many different passwords are possible?

$$ 26^3$ \times 10^2$ = 175,760 $$

Question 1

Which of the following best describes a probability experiment?

Accepted Answer

An action or trial through which specific results (counts, measurements, or responses) are obtained.

Question 2

A company surveys 2000 people about their favorite fruit. 600 people choose apples. What is the empirical probability that a randomly selected person prefers apples?

Accepted Answer

$$ P(	ext{apples}) = \frac{600}{2000} = 0.3 $$

Question 3

Which of the following is an example of subjective probability?

Accepted Answer

A doctor estimates a patient has a 90% chance of recovery based on experience.

Question 4

If a password consists of 3 letters followed by 2 digits (0-9), and letters and digits can be repeated, how many different passwords are possible?

Accepted Answer

$$ 26^3$ 	imes 10^2$ = 175,760 $$

Question 5

Which of the following statements about the Law of Large Numbers is correct?

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Which of the following is NOT a property of probability?

Accepted Answer

The probability of any event is always greater than 1.

Question 8

A blood test can be positive or negative. If there are 4 blood types and each can be positive or negative, how many possible outcomes are there?

Accepted Answer

$$ 4 	imes 2 = 8 $$

Question 9

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

Accepted Answer

$$ 1 - 0.7 = 0.3 $$

Question 10

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

Accepted Answer

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

Question 11

Which of the following best describes a simple event?

Accepted Answer

An event that consists of a single outcome.

Question 12

A spinner has 5 equal sections numbered 1 to 5. What is the classical probability of spinning a 4?

Accepted Answer

$$ \frac{1}{5} $$

Question 13

A survey finds that 765 out of 3000 users are aged 25 to 34. What is the probability that the next user surveyed is 25 to 34 years old?

Accepted Answer

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

Question 14

Which of the following is an example of empirical probability?

Accepted Answer

The probability that a randomly chosen voter is under 35 is 0.3, based on survey data.

Question 15

If you roll a die and flip a coin, how many possible outcomes are there?

Accepted Answer

$$ 6 	imes 2 = 12 $$

Chapter 3: Probability – Structured Study Notes for Introductory Statistics

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