Events A and B are mutually exclusive.Which of the following statements is also true?

A) A and B are also independent.
B) P(A ∪ B) = P(A) P(B)
C) P(A ∪ B) = P(A) + P(B)
D) P(A ∩ B) = P(A) + P(B)

Question

Shante Williams · Accepted Answer

Final Answer : C, Explanation :  Since events A and B are mutually exclusive, they cannot occur at the same time, which means that the probability of either A or B happening (their union) is equal to the sum of their individual probabilities. Therefore, P(A ∪ B) = P(A) + P(B) is the correct statement. Choices A and B are not true because mutually exclusive events cannot be independent (if one occurs, the other cannot) and their joint probability (P(A ∩ B)) is equal to 0. Choice D is also false because the probability of two mutually exclusive events intersecting is always 0.

Events A and B are mutually exclusive.Which of the following statements is also true?

A) A and B are also independent.
B) P(A ∪ B) = P(A) P(B)
C) P(A ∪ B) = P(A) + P(B)
D) P(A ∩ B) = P(A) + P(B)

Definitions

Learning Objectives

Learning Objectives

Related questions

Events A and B are mutually exclusive.Which of the following statements is also true?A) A and B are also independent.B) P(A ∪ B) = P(A) P(B) C) P(A ∪ B) = P(A) + P(B) D) P(A ∩ B) = P(A) + P(B)

Definitions

Learning Objectives

Learning Objectives

Related questions

Events A and B are mutually exclusive.Which of the following statements is also true?

A) A and B are also independent.
B) P(A ∪ B) = P(A) P(B)
C) P(A ∪ B) = P(A) + P(B)
D) P(A ∩ B) = P(A) + P(B)