CBSE 2025 · Region 7 · Set 1 · Q38 · 4 marks
Based upon the results of regular medical check-ups in a hospital, it was found that out of $\displaystyle 1000$ people, $\displaystyle 700$ were very healthy, $\displaystyle 200$ maintained average health and $\displaystyle 100$ had a poor health record. Let $\displaystyle \mathrm{A}_{1}$ : People with good health, $\displaystyle \mathrm{A}_{2}$ : People with average health, and $\displaystyle \mathrm{A}_{3}$ : People with poor health. During a pandemic, the data expressed that the chances of people contracting the disease from category $\displaystyle \mathrm{A}_{1}, \mathrm{~A}_{2}$ and $\displaystyle \mathrm{A}_{3}$ are $\displaystyle 25 \%, 35 \%$ and $\displaystyle 50 \%$, respectively. Based upon the above information, answer the following questions :(i)A person was tested randomly. What is the probability that he/she has contracted the disease?(ii)Given that the person has not contracted the disease, what is the probability that the person is from category $\displaystyle \mathrm{A}_{2}$ ?
Based upon the results of regular medical check-ups in a hospital, it was found that out of $\displaystyle 1000$ people, $\displaystyle 700$ were very healthy, $\displaystyle 200$ maintained average health and $\displaystyle 100$ had a poor health record. Let $\displaystyle \mathrm{A}_{1}$ : People with good health, $\displaystyle \mathrm{A}_{2}$ : People with average health, and $\displaystyle \mathrm{A}_{3}$ : People with poor health. During a pandemic, the data expressed that the chances of people contracting the disease from category $\displaystyle \mathrm{A}_{1}, \mathrm{~A}_{2}$ and $\displaystyle \mathrm{A}_{3}$ are $\displaystyle 25 \%, 35 \%$ and $\displaystyle 50 \%$, respectively. Based upon the above information, answer the following questions :
(i)
A person was tested randomly. What is the probability that he/she has contracted the disease?
(ii)
Given that the person has not contracted the disease, what is the probability that the person is from category $\displaystyle \mathrm{A}_{2}$ ?
Marking-scheme solution
(i)
Let A: Person contracted the disease
\[\begin{aligned}
P(\mathrm{A}) & =P\left(\mathrm{A}_{1}\right) \cdot P\left(\mathrm{A} \mid \mathrm{A}_{1}\right)+P\left(\mathrm{A}_{2}\right) \cdot P\left(\mathrm{A} \mid \mathrm{A}_{2}\right)+P\left(\mathrm{A}_{3}\right) \cdot P\left(\mathrm{A} \mid \mathrm{A}_{3}\right) \\
& =\frac{7}{10}\left(\frac{25}{100}\right)+\frac{2}{10}\left(\frac{35}{100}\right)+\frac{1}{10}\left(\frac{50}{100}\right) \\
& =\frac{295}{1000}=0.295 \text { or }\left(\frac{59}{200}\right)
\end{aligned}
\]
ProbabilityBayes' TheoremApplycase_studymedium
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CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.