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

Question 1

Which of the following best describes the relationship between events A and B in the FIRST Venn diagram (with overlapping circles)?

Accepted Answer

Events A and B are not disjoint; they can occur together.

Question 2

In the SECOND Venn diagram (with non-overlapping circles), what is the probability of both events A and B occurring?

Accepted Answer

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

Question 3

Which addition rule formula is illustrated by the FIRST Venn diagram?

Accepted Answer

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

Question 4

If events A and B are represented by the SECOND Venn diagram, which statement is true?

Accepted Answer

Events A and B are disjoint (mutually exclusive).

Question 5

Suppose $$P(A) = 0.3$$ and $$P(B) = 0.4. If $$events A and B are disjoint, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.7$$

Question 6

Suppose $$P(A) = 0.5$$, $$P(B) = 0.6$$, and $$P(A \cap B) = 0.2. $$What is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.9$$

Question 7

Which of the following is a necessary condition for using the formula $$P(A 	ext{ or } B) = P(A) + P(B)$$ without subtracting $$P(A \cap B)$$?

Accepted Answer

Events A and B are disjoint.

Question 8

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

Accepted Answer

$$0$$

Question 9

Which real-life scenario best matches the SECOND Venn diagram (disjoint events)?

Accepted Answer

Selecting a card that is both a heart and a diamond from a standard deck.

Question 10

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.1$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.7$$

Introductory Statistics Probability and Counting Rules Study Guide

Study Guide - Practice Questions