P ( A ∪ B )= P ( A ∩ B ) if and only if

Question

P ( A ∪ B )= P ( A ∩ B ) if and only if (A) P(A)=P(B)=P(A ∩ B) (B) P ( A )= P ( B )=(1/2) (C) P(A)+P(B)=1 (D) P ( A ∩ overline B )= P ( overline A ∩ B )=0

Tardigrade Admin · Accepted Answer

P(A ∪ B)=P(A ∩ B) P(A)+P(B)-P(A ∩ B)=P(A ∩ B) P(A)+P(B)=2 P(A ∩ B) ⇒ (A) P(A)-P(A ∩ B)=0 P(A ∩ barB)=0 ⇒ text (D)

Q. $P (A \cup B) = P (A \cap B)$ if and only if

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

$P (A) = P (B) = \frac{1}{2}$

$P (A) + P (B) = 1$

$P (A \cap \overline{B}) = P (\overline{A} \cap B) = 0$

$P (A \cup B) = P (A \cap B)$
$P (A) + P (B) - P (A \cap B) = P (A \cap B)$
$P (A) + P (B) = 2 P (A \cap B) \Rightarrow (A)$
$P (A) - P (A \cap B) = 0$
$P (A \cap \overset{ˉ}{B}) = 0 \Rightarrow (D)$

Q. P(A∪B)=P(A∩B) if and only if

P(A)=P(B)=P(A∩B)

P(A)=P(B)=21​

P(A)+P(B)=1

P(A∩B)=P(A∩B)=0