Question

If A and B are any two events, then the probability that exactly one of them occur is

• A. $P ( A ) + P ( B ) - P ( A \cap B )$
• B. $P ( A ) + P ( B ) - 2 P ( A \cap B )$
• C. $P ( A ) + P ( B ) - P ( A \cup B )$
• D. $P ( A ) + P ( B ) - 2 P ( A \cup B )$

Answer 1

Answer: (B)

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

Answer 2

Required probability $= A$ occurs and does not occur or B occurs and $A$ does not occur

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

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

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