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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Sets and Relations

JEE Main · Mathematics · Sets and Relations

The chances to fail in Physics are 20 \% and the chances to fail in...

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?

Options

A $28 \%$
B $38 \%$
C $72 \%$
D $82 \%$

Correct answer

A. $28 \%$

Step-by-step solution

Let

P(A)=\frac{20}{100}=\frac{1}{5}, P(B)=\frac{10}{100}=\frac{1}{10}

Since, event are independent and we have to

\text { find }

\begin{aligned}P(A&\cup B)=P(A)+P(B)-P(A) \cdotP(B) \\ &=\frac{1}{5}+\frac{1}{10}-\frac{1}{5} \cdot \frac{1}{10}\\ &=\frac{3}{10}-\frac{1}{50}=\frac{14}{50}=\frac{14}{50} \times100=28 \% \end{aligned}

$

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