If A and B are any two events such that P(A) + P(B) - P(A B) = P(A), then (A) P(B|A) = 1 (B) P(A|B) = 1 (C) P(B|A) = 0 (D) P(A|B) = 0

Option B is correct P(A) + P(B) - P(A B) = P(A) P(B) - P(A B) = 0 P(A B) = P(B) P(B) = 1 P(A/B) = 1

Probability — Class 12 Maths Solution

ncert misc SA NCERT,Misc,Q.19,Page.584

Question

If $A$ and $B$ are any two events such that
$P(A) + P(B) - P(A{\rm{ and }}B) = P(A),$ then

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

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

(D) $P(A|B) = 0$

Step-by-step Solution

Option B is correct

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

$\Rightarrow P(B) - P(A \cap B) = 0$

$\Rightarrow P(A \cap B) = P(B) \Rightarrow \cfrac{{P(A \cap B)}}{{P(B)}} = 1 \Rightarrow P(A/B) = 1$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Probability. Curated by Sachin Sharma. Free for all students.