Q: Which formula correctly represents the General Addition Rule (GAR) for any two events A and B?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Question 1

Which of the following best describes the sample space in a probability experiment?

Accepted Answer

The set of all possible outcomes of the experiment.

Question 2

Suppose you roll a fair six-sided die. What is the probability of rolling an even number?

Accepted Answer

$$\frac{1}{2}$$

Question 3

If two events A and B are mutually exclusive, which of the following is true?

Accepted Answer

$$P(A 	ext{ and } B) = 0$$

Question 4

Given $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.9$$

Question 5

Which formula correctly represents the General Addition Rule (GAR) for any two events A and B?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 6

A group of 5 people (Adam, Beth, Carl, Dana, Ethan) forms a team of 3. What is the probability that Adam is chosen?

Accepted Answer

$$\frac{3}{10}$$

Question 7

Which Venn diagram (from the images above) best represents mutually exclusive events?

Accepted Answer

The diagram where circles A and B do not overlap.

Question 8

If $$P(E) = 0.7$$, what is $$P(	ext{not } E)$$?

Accepted Answer

$$0.3$$

Question 9

Which of the following is NOT a property of probability?

Accepted Answer

The probability of an event can be greater than 1.

Question 10

In a survey of 100 students, 35 took History, 55 took Math, and 20 took both. What is the probability that a randomly selected student took neither History nor Math?

Accepted Answer

$$0.3$$

Question 11

If $$P(A) = \frac{1}{4}$$, $$P(B) = \frac{1}{3}$$, and $$P(A 	ext{ or } B) = \frac{1}{2}$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$\frac{1}{12}$$

Question 12

Which rule should be used to find $$P(A 	ext{ or } B)$$ when A and B are not mutually exclusive?

Accepted Answer

General Addition Rule (GAR)

Question 13

If three events A, B, and C are mutually exclusive, which of the following is true?

Accepted Answer

$$P(A 	ext{ and } B) = 0$$

Question 14

A Venn diagram shows two overlapping circles labeled A and B. What does the overlapping region represent?

Accepted Answer

Outcomes common to both A and B.

Question 15

Which of the following is the correct formula for the number of ways to choose r items from n items (combinations)?

Accepted Answer

$$\frac{n!}{r!(n-r)!}$$

Probability Basics and Rules: Study Notes for Introductory Statistics

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