If A and B are two events, the probabili

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

If A and B are two events, the probability that exactly one of them occurs is given by

Options:

$P(A)+P(B)-2 P(A \cap B)$

$P\left(A \cap B'\right)-P\left(A' \cap B\right)$

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

$P\left(A'\right)+P\left(B'\right)+2 P\left(A' \cap B'\right)$

Correct Answer:

$P(A)+P(B)-2 P(A \cap B)$

Explanation:

$P(A \bar{B} \cup \bar{A} B)=P(A)-P(A B)+P(B)-P(A B)$

$=P(A)+P(B)-2 P(A B)$