CBSE 2026 · Region 5 · Set 1 · Q37 · 4 marks
There are three types of vaccines $\displaystyle \mathrm{A}_{1}, \mathrm{~A}_{2}, \mathrm{~A}_{3}$, available in the market to protect the population of the country from spread of certain infection. According to a survey conducted, it was found that $\displaystyle 25$% of the population was given Vaccine $\displaystyle \mathrm{A}_{1}, 35 \%$ of the population was given Vaccine $\displaystyle \mathrm{A}_{2}$ and $\displaystyle 40$% of the population was given Vaccine $\displaystyle \mathrm{A}_{3}$. The survey also stated that the probabilities that Vaccines $\displaystyle \mathrm{A}_{1}, \mathrm{~A}_{2}$ and $\displaystyle \mathrm{A}_{3}$ would protect against the infection were $\displaystyle 60$%, $\displaystyle 55$% and $\displaystyle 50$% respectively. Based on the above information, answer the following questions : Find the probability that :(i)The person taking vaccine $\displaystyle \mathrm{A}_{2}$ will get infected.(ii)If a person is chosen randomly, he/she will be protected from the infection.(iii)The person was given Vaccine $\displaystyle \mathrm{A}_{1}$, given that the randomly chosen person is infected.The person was given Vaccine $\displaystyle \mathrm{A}_{3}$, given that the randomly chosen person is not infected. Case Study - $\displaystyle 3$
There are three types of vaccines $\displaystyle \mathrm{A}_{1}, \mathrm{~A}_{2}, \mathrm{~A}_{3}$, available in the market to protect the population of the country from spread of certain infection. According to a survey conducted, it was found that $\displaystyle 25$% of the population was given Vaccine $\displaystyle \mathrm{A}_{1}, 35 \%$ of the population was given Vaccine $\displaystyle \mathrm{A}_{2}$ and $\displaystyle 40$% of the population was given Vaccine $\displaystyle \mathrm{A}_{3}$. The survey also stated that the probabilities that Vaccines $\displaystyle \mathrm{A}_{1}, \mathrm{~A}_{2}$ and $\displaystyle \mathrm{A}_{3}$ would protect against the infection were $\displaystyle 60$%, $\displaystyle 55$% and $\displaystyle 50$% respectively. Based on the above information, answer the following questions : Find the probability that :
(i)
The person taking vaccine $\displaystyle \mathrm{A}_{2}$ will get infected.
(ii)
If a person is chosen randomly, he/she will be protected from the infection.
(iii)
The person was given Vaccine $\displaystyle \mathrm{A}_{1}$, given that the randomly chosen person is infected.
The person was given Vaccine $\displaystyle \mathrm{A}_{3}$, given that the randomly chosen person is not infected. Case Study - $\displaystyle 3$
Marking-scheme solution
(i)
P (Person taking vaccine $\displaystyle A_{2}$ will be infected) $\displaystyle =45\%$ or $\displaystyle 0 \cdot 45$
(ii)
P (Person is protected from infection) $\displaystyle =\dfrac{25}{100} \cdot \dfrac{60}{100}+\dfrac{35}{100} \cdot \dfrac{55}{100}+\dfrac{40}{100} \cdot \dfrac{50}{100}$
$\displaystyle =\dfrac{5425}{10000}$ or $\displaystyle 0 \cdot 5425$
(iii)
$\displaystyle P\left(A_{1} \mid\right.$ person is infected $\displaystyle )=\dfrac{\dfrac{25}{100} \cdot \dfrac{40}{100}}{\dfrac{25}{100} \cdot \dfrac{40}{100}+\dfrac{35}{100} \cdot \dfrac{45}{100}+\dfrac{40}{100} \cdot \dfrac{50}{100}}$
$\displaystyle =\dfrac{1000}{4575}$ or $\displaystyle \dfrac{40}{183}$
$\displaystyle P\left(A_{3} \mid\right.$ person is not infected $\displaystyle )=\dfrac{\dfrac{40}{100} \cdot \dfrac{50}{100}}{\dfrac{25}{100} \cdot \dfrac{60}{100}+\dfrac{35}{100} \cdot \dfrac{55}{100}+\dfrac{40}{100} \cdot \dfrac{50}{100}}$
$\displaystyle =\dfrac{2000}{5425}$ or $\displaystyle \dfrac{80}{217}$
ProbabilityBayes' TheoremApplycase_studymedium
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.