Assertion (A): If A and B are mutually exclusive, P(A B) = P(A) + P(B). Reason (R): Mutually exclusive events have P(A B) = 0.

Question 66

MediumOriginal question

Assertion (A): If $A$ and $B$ are mutually exclusive, $P(A \cup B) = P(A) + P(B)$ .
Reason (R): Mutually exclusive events have $P(A \cap B) = 0$ .

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

In $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ , the last term is 0 for mutually exclusive events.
So R is true and explains A.

Concept: The addition rule for mutually exclusive events
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe addition and complement rules

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Assertion (A): If AAA and BBB are mutually exclusive, P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B)P(A∪B)=P(A)+P(B).Reason (R): Mutually exclusive events have P(A∩B)=0P(A \cap B) = 0P(A∩B)=0.

Explanation

Assertion (A): If $A$ and $B$ are mutually exclusive, $P(A \cup B) = P(A) + P(B)$ .
Reason (R): Mutually exclusive events have $P(A \cap B) = 0$ .