Question

A, B, C are any three events. If P (S) denotes the probability of S happening then $P ( A \cap ( B \cup C ) ) =$

• A. $P ( A ) + P ( B ) + P ( C ) - P ( A \cap B ) - P ( A \cap C )$
• B. $P ( A ) + P ( B ) + P ( C ) - P ( B ) P ( C )$
• C. $P ( A \cap B ) + P ( A \cap C ) - P ( A \cap B \cap C )$
• D. None of these

Answer 1

Answer: (C)

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

Answer 2

$P [ A \cap ( B \cup C ) ] = P [ ( A \cap B ) \cup ( A \cap C ) ]$

$= P ( A \cap B ) + P ( A \cap C ) - P [ ( A \cap B ) \cap ( A \cap C ) ]$

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