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A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) = 0.35. Find (ii) P(A´ ∩ B´)

7.(ii)  A and B are two events such that $\small P(A)=0.54$,  $\small P(B)=0.69$ and  $\small P({A}\cap {B})=0.35$. Find (ii)  $\small P({A}'\cap {B}')$

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Given, $P(A) = 0.54, P(B) = 0.69, P(A \cap B) = 0.35$

And, $P(A \cup B) = 0.88$

(ii) $A' \cap B'= (A \cup B)'$  [De Morgan’s law]

So, $P(A' \cap B') = P(A \cup B)' = 1 - P(A \cup B) = 1 - 0.88 = 0.12$

$\therefore$  $P(A' \cap B') = 0.12$

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