Evaluate (A B) , if 2P(A) = P(B) = 13 and P(A|B) = 5

.: Given, P(A|B) = 5 P(B) = 5 P(A B) = 5 P(B) = 5 13 = 13 Hence, P(A B) = P(A) + P(B) - P(A B) = 2 13 + 13 - 13 = 26 = 26

Probability — Class 12 Maths Solution

ncert exercise SA NCERT,EX.13.1,Q.4,Page.538

Question

Evaluate $(A \cup B)$ , if $2P(A) = P(B) = \cfrac{5}{{13}}$ and $P(A|B) = \cfrac{2}{5}$

Step-by-step Solution

.: Given, $P(A|B) = \cfrac{2}{5} \Rightarrow \cfrac{{P(A \cap B)}}{{P(B)}} = \cfrac{2}{5}$

$\Rightarrow P(A \cap B) = \cfrac{2}{5}P(B) = \cfrac{2}{5} \times \cfrac{5}{{13}} = \cfrac{2}{{13}}$

Hence, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$= \cfrac{1}{2} \times \cfrac{5}{{13}} + \cfrac{5}{{13}} - \cfrac{2}{{13}}$

$= \cfrac{{5 + 10 - 4}}{{26}} = \cfrac{{11}}{{26}}$

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