Question

If $ 0 < P(A) < 1,0 < P(B) < 1$ and $P (A \cap B) = P(A) + P(B) - P(A) P(B)$, then

• A. $P(B/A) = P(B) - P(A)$
• B. $P(A ' - B') = P(A ') - P(B ')$
• C. $P (A\cup B ) '= P(A)'P(B)'$
• D. $P(A / B) = P(A) - P(B)$

Answer 1

Answer: (B)

Since, $P(A \cap B) = P(A) P(B)$
It means $A$ and $B$ are independent events, so $A$ ' and $B$ ' are also independent.
$\therefore P(A \cup B)' =P(A ' \cup B ') = P(A)' . P(B)'$
Alternate Solution
$P (A \cup B )' = l - P ( A \cup B ) = 1 - [P(A) + P(B) -P(A).P(B) $
$={1 - P(A)}{1 - P(B)} = P(A)' P(B)'$