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Home  >>  CBSE XII  >>  Math  >>  Probability

If $P(A)=\Large\frac{2}{5},\normalsize P(B)=\Large\frac{3}{10}$ and $P(A\cap B)=\Large\frac{1}{5},$then P(A|B).P(B'|A') is equal to

$\begin{array}{1 1}(A)\;\large\frac{5}{6}\\(B)\;\large\frac{5}{7}\\(C)\;\large\frac{25}{42}\\(D)\;1\end{array} $

1 Answer

Toolbox:
  • P(A/B)=\(\frac{P(A(\cap)B)}{P(B)}\)
  • P\(\bar{A}\)=1-P(A)
  • P(A\(\cup\)B)=P(A)+P(B)-P(A\(\cap\)B)
P(A/B)=\(\frac{1}{5}\)\(\times\)\(\frac{10}{3}\)
=\(\frac{2}{3}\)
p(A\(\cup\)B)=\(\frac{3}{10}\)+\(\frac{2}{3}\)-\(\frac{3}{5}\)
=\(\frac{1}{10}\)
 
 
p(\(\bar{A}\))=\(\large\frac{1}{0}\)-\(\frac{2}{5}\)=\(\frac{3}{5}\)
=\(\large\frac{1}{}\)-\(\frac{1}{10}\)=\(\frac{3}{10}\)
=\(\large\frac{9}{10}\)
P(\(\overline{B\cup\;A}\))=\(\large\frac{9}{10}\)\(\times\)\(\frac{5}{3}\)
=\(\frac{3}{2}\)
P(A/B)P(\(\bar{A}\)/\(\bar{B}\))=\(\large\frac{2}{3}\)\(\frac{2}{3}\)
=1
'D'option is correct

 

answered Feb 23, 2013 by poojasapani_1
edited Jun 4, 2013 by poojasapani_1
 

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