If P(A) = 11 , ;P(B) = 11 ; ;P(A B) = 11 , find (i) P(A B) (ii) P(A|B) (iii) P(B|A)

.: (i) Given, P(A B) = 11 P(A) + P(B) - P(A B) = 11 11 + 11 - P(A B) = 11 P(A B) = 11 + 11 - 11 = 11 P(A B) = 11 + 11 - 11 = 11 (ii) P(A/B) = P(B) = 5/11 = 5 (iii) P(B/A) = P(A) = 6/11 = 6 = 3

Probability — Class 12 Maths Solution

ncert exercise SA NCERT,EX.13.1,Q.5,Page.538

Question

If $P(A) = \cfrac{6}{{11}},\;P(B) = \cfrac{5}{{11}}\;{\rm{and}}\;P(A \cup B) = \cfrac{7}{{11}}$ , find

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

(ii) $P(A|B)$

(iii) $P(B|A)$

Step-by-step Solution

.: (i) Given, $P(A \cup B) = \cfrac{7}{{11}}$

$\Rightarrow$ $P(A) + P(B) - P(A \cap B) = \cfrac{7}{{11}}$

$\Rightarrow$ $\Rightarrow \cfrac{6}{{11}} + \cfrac{5}{{11}} - P(A \cap B) = \cfrac{7}{{11}}$

$\Rightarrow P(A \cap B) = \cfrac{6}{{11}} + \cfrac{5}{{11}} - \cfrac{7}{{11}} = \cfrac{4}{{11}}$ $P(A \cap B) = \cfrac{6}{{11}} + \cfrac{5}{{11}} - \cfrac{7}{{11}} = \cfrac{4}{{11}}$

(ii) $P(A/B) = \cfrac{{P(A \cap B)}}{{P(B)}} = \cfrac{{4/11}}{{5/11}} = \cfrac{4}{5}$

(iii) $P(B/A) = \cfrac{{P(A \cap B)}}{{P(A)}} = \cfrac{{4/11}}{{6/11}} = \cfrac{4}{6} = \cfrac{2}{3}$

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