Q66 / 150 · MHT CET 2008 · Mathematics
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?
- Correct answerA$28 \%$
- B$38 \%$
- C$72 \%$
- D$82 \%$
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
$$
\text { find } \begin{aligned}
P(A&\cup B)=P(A)+P(B)-P(A) \cdot P(B) \\
&=\frac{1}{5}+\frac{1}{10}-\frac{1}{5} \cdot \frac{1}{10} \\
&=\frac{3}{10}-\frac{1}{50}=\frac{14}{50}=\frac{14}{50} \times 100=28 \%
\end{aligned}
$$
Hence, the correct answer is option: 'A'.