If P(A) = 10 , P(B) = 5 and P(A B) = 5 , then P(B/A) + P(A/B) equals to

Here, P(A) = 10 ,P(B) 5 and P(A B) = 5 P(B/A) + P(A/B) = P(A) + P(B) = P(A) + P(B) = 10 + 5 - 5 10 + 10 + 5 - 5 5 = 10 10 + 10 5 = 3 + 4 = 12

Probability — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.58,Page.279

Question

If $P(A) = \frac{3}{{10}}$, $P(B) = \frac{2}{5}$ and $P(A \cup B) = \frac{3}{5}$,

then $P(B/A) + P(A/B)$ equals to

Step-by-step Solution

Here, $P(A) = \frac{3}{{10}},P(B)\frac{2}{5}$

and $P(A \cup B) = \frac{3}{5}$

$P(B/A) + P(A/B) = \frac{{P(B \cap A)}}{{P(A)}} + \frac{{P(A \cap B)}}{{P(B)}}$

$= \frac{{P(A) + P(B) - P(A \cup B)}}{{P(A)}} + \frac{{P(A) + P(B) - P(A \cup B)}}{{P(B)}}$

$= \frac{{\frac{3}{{10}} + \frac{2}{5} - \frac{3}{5}}}{{\frac{3}{{10}}}} + \frac{{\frac{3}{{10}} + \frac{2}{5} - \frac{3}{5}}}{{\frac{2}{5}}}$

$= \frac{{\frac{1}{{10}}}}{{\frac{3}{{10}}}} + \frac{{\frac{1}{{10}}}}{{\frac{2}{5}}} = \frac{1}{3} + \frac{1}{4} = \frac{7}{{12}}$

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