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

Option A is correct P(B|A) = 1 P(A) = 1 P(A B) = P(A) A B [ When A B , then A B = A ]

Probability — Class 12 Maths Solution

ncert misc SA NCERT,Misc,Q.17,Page.584

Question

If $A$ and $B$ are two events such that $P(A) \ne 0$ and $P(B|A) = 1,$ then

(A) $A \subset B$

(B ) $B \subset A$

(D) $A = \phi$

Step-by-step Solution

Option A is correct

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

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

[ When $A \subset B$ , then $A \cap B = A$ ]

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