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# In a college,30% students fail in physics,25% fail in mathematics and 10% fail in both.One student is chosen at random.The probability that she fails in physics if she has failed in mathematics is

$\begin{array}{1 1} (A)\;\large\frac{1}{10}\quad(B)\;\large\frac{2}{5}\quad (C)\;\large\frac{9}{20}\quad(D)\;\;\large\frac{1}{3}\end{array}$

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A)
Toolbox:
• If $E$ and $F$ are two events associated with sample space.
• The conditional probability of event $E$ under the condition that event $F$ has occured is given by
• $p(E/F)=\Large\frac{p(E\cap F)}{p(F)}$
• $p(F)\neq 0$
p(student fails in Physics)=p(E)$=30\%=\large\frac{30}{100}$
p(student fails in Mathematics)=p(F)$=25\%=\large\frac{25}{100}$
p(fails both in Physics and Mathematics)$=p(E\cap F)=10\%=\large\frac{10}{100}$
p(Fails in Physics given tails in Mathmatics)
$p(E/F)=\Large\frac{p(E\cap F)}{p(F)}$
=$\Large\frac{10/100}{25/100}$
=$\Large\frac{2}{5}$
$'B'$ option is correct