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# The chances to fail in Physics are 20% and the chances to fail in Mathematics are 10%. What are the chances to fail in at least one subject ?

$\begin {array} {1 1} (A)\;28\: \% & \quad (B)\;38\: \% \\ (C)\;72\: \% & \quad (D)\;82\: \% \end {array}$

Let $P(A) = \large\frac{20}{100}$
= $\large\frac{1}{5}$
P(B) = $\large\frac{10}{100}$
= $\large\frac{1}{10}$
Since event are independent
$\therefore P(A \cup B ) = 1-P(A')\: P(B')$
$\Rightarrow P(A \cup B)=1-\large\frac{4}{5}.\large\frac{9}{10}$
$= 1-\large\frac{36}{50}$
$= \large\frac{14}{50} = 28 \%$
Ans : (A)