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Home  >>  CBSE XII  >>  Math  >>  Probability
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If $P(A)=\Large\frac{3}{10},\normalsize P(B)=\Large\frac{2}{5}$ and $P(A\cap B)=\Large\frac{3}{5},$then $P(B|A)+P(A|B)$ equals

$\begin{array}{1 1}(A)\;\large\frac{1}{4}\quad(B)\;\large\frac{1}{3}\quad(C)\;\large\frac{5}{12}\quad(D)\;\large\frac{7}{2}\end{array} $

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1 Answer

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Toolbox:
  • P(A\(\cap\)B)=P(A)+P(B)-P(A\(\cap\)B)
  • \(\large\;p(A/B)=\;\frac{p(A(\cap)B)}{p(A)}\)
  • \(large\;P(B/A)=\;\frac{P(A(\cap)B)}{P(B)}\)
\(\large\frac{3}{5}\)=\(\large\frac{3}{10}\)+\(\frac{2}{5}\)-P(A\(\cap\)B)
P(A\(\cap\)B)=\(\large\frac{3}{10}\)+\(\frac{7}{5}\)-\(\frac{3}{5}\)
=\(\large\frac{1}{10}\)
P(B/A)=\(\large\frac{1}{10}\)x\(\frac{10}{3}\)
=\(\large\frac{1}{3}\)
P(A/B)=\(\large\frac{1}{10}\)x\(\frac{5}{2}\)
=\(\large\frac{1}{4}\)
P(A/B)+P(B/A)=\(\frac{1}{4}\)+\(\frac{1}{3}\)
=\(\frac{7}{12}\)
'd' is correct option

 

answered Feb 23, 2013 by poojasapani_1
edited Mar 14, 2013 by poojasapani_1
 

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