Q: If two events $$A$$ and $$B$$ are independent, which statement is true?

$$P(A \cap B) = P(A) \times P(B)$$

Question 1

Which of the following best describes theoretical probability?

Accepted Answer

Probability determined by analyzing a mathematical model of all possible outcomes.

Question 2

A computer randomly selects a number between 1 and 100. What type of probability is being used?

Accepted Answer

Theoretical probability

Question 3

Which scenario best illustrates the concept of randomness?

Accepted Answer

A die is rolled and the outcome is recorded.

Question 4

If $$A$$ and $$B$$ are mutually exclusive events, what is $$P(A \cap B)$$?

Accepted Answer

$$P(A \cap B) = 0$$

Question 5

Which of the following is NOT a requirement for a set of events to be considered independent?

Accepted Answer

The events must be mutually exclusive.

Question 6

A medical test for a disease is positive in 5% of healthy people and 95% of sick people. If a person tests positive, which probability concept helps determine the chance they are actually sick?

Accepted Answer

Conditional probability

Question 7

Which formula correctly represents the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 8

In a survey, 60% of respondents like tea, 40% like coffee, and 20% like both. What is the probability that a randomly selected respondent likes either tea or coffee?

Accepted Answer

$$0.80$$

Question 9

Which of the following best describes a simulation in statistics?

Accepted Answer

A method of using random numbers to model and study complex systems.

Question 10

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 11

Which of the following is an example of a conditional probability?

Accepted Answer

The probability that a student is left-handed given that they play tennis.

Question 12

A bag contains 3 red balls and 7 blue balls. If one ball is drawn at random, what is the theoretical probability it is red?

Accepted Answer

$$0.3$$

Question 13

Which statement about mutually exclusive events is true?

Accepted Answer

Their intersection is always empty.

Question 14

A researcher flips a coin 100 times and gets 48 heads. What is the empirical probability of getting heads?

Accepted Answer

$$0.48$$

Question 15

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 16

If $$P(A|B) = 0.4$$ and $$P(B) = 0.5$$, what is $$P(A \cap B)$$?

Accepted Answer

$$0.2$$

Question 17

Which of the following is NOT a categorical variable?

Accepted Answer

Height in centimeters

Question 18

A study finds that 30% of people who exercise regularly also eat vegetables daily. What type of probability is this?

Accepted Answer

Conditional probability

Question 19

Which of the following is an example of aggregate data?

Accepted Answer

The average test score of a class.

Question 20

If two events $$A$$ and $$B$$ are independent, which statement is true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Foundations of Probability and Categorical Associations

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