MHT CET · Maths · Sets and Relations
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?
- A \(28 \%\)
- B \(38 \%\)
- C \(72 \%\)
- D \(82 \%\)
Answer & Solution
Correct Answer
(A) \(28 \%\)
Step-by-step Solution
Detailed explanation
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
find \(P(A\cup B)=P(A)+P(B)-P(A) \cdot P(B) \)
\( =\frac{1}{5}+\frac{1}{10}-\frac{1}{5} \cdot \frac{1}{10} \)
\( =\frac{3}{10}-\frac{1}{50}=\frac{14}{50}=\frac{14}{50} \times 100=28 \%\)
Since, event are independent and we have to
find \(P(A\cup B)=P(A)+P(B)-P(A) \cdot P(B) \)
\( =\frac{1}{5}+\frac{1}{10}-\frac{1}{5} \cdot \frac{1}{10} \)
\( =\frac{3}{10}-\frac{1}{50}=\frac{14}{50}=\frac{14}{50} \times 100=28 \%\)
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