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Home  >>  CBSE XII  >>  Math  >>  Probability
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If \( P(A) = \large \frac{6}{11} \)\(, P(B) =\large \frac{5}{11}\:\) and \( P(A \cup B) = \large \frac{7}{11}\) , find (i) P(A \( \cap\) B) , (ii) P(A|B) , (iii) P(B|A)

$\begin{array}{1 1} \text{(i) 4/11, (ii) 2/11, (iii) 3/11} \\ \text{(i) 4/11, (ii) 4/5, (iii) 2/3} \\ \text{(i) 7/11, (ii) 3/5, (iii) 2/3} \\ \text{(i) 7/11, (ii) 3/5, (iii) 4/5} \end{array} $

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  • \(1)\;p(A\cup\;B)=p(A)\;+\;p(B)\;-\;p(A\;\cap\;B)\) \(\Rightarrow\;p(A\;\cap\; B)=p(A)\;+\;p(B)\;-\;p(A\;\cup\;B)\)
  • \(2)\;p(A/B)=\large\frac{p(A\;\cap\;B)}{p(B)}\)
  • \(3)\;p(B/A)=\large\frac{p(A\;\cap\;B)}{p(A)}\)
Given $p(A) = \large\frac{6}{11}$ and $p(B) = \large\frac{5}{11}$, $p(A\;\cup\;B) = \large\frac{7}{11}$
Therefore, \(p(A\cap\;B)=\large\frac{6}{11}\;+\;\frac{5}{11}\;-\;\frac{7}{11}\;=\;\frac{4}{11}\)
\(p(A/B)=\Large \frac{\frac{4}{11}}{\frac{5}{11}}\) =\(\large\frac{4}{5}\)
\(p(B/A)=\Large \frac{\frac{4}{11}}{\frac{6}{11}}\) =\(\large \frac{2}{3}\)
answered Mar 20, 2013 by poojasapani_1
edited Jun 18, 2013 by balaji.thirumalai
 

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