✓ Board-verified
Mathematics · 2026 · 4 marks
CBSE 2026 · Region 5 · Set 1 · Q37
There are three types of vaccines A_1, A_2, A_3, available in the market to protect the population of the country from spread of certain infection.…
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)
(a)
The person was given Vaccine $\displaystyle \mathrm{A}_{1}$, given that the randomly chosen person is infected.
OR
(b)
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)
(a)
$\displaystyle P\left(A_{1} \mid\right.$ 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 $\displaystyle \dfrac{40}{183}$
OR
(b)
$\displaystyle P\left(A_{3} \mid\right.$ 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 $\displaystyle \dfrac{80}{217}$
More from Probability
- Assertion: Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is 1/3. Reason…2023
- If A and B are two events such that P(B)=1/5, P(A ∣ B)=2/3 and P(A ∪ B)=3/5, then P(A) is:2025
- A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances of their manufacturing a defective…2025
- Three friends A, B and C got their photograph clicked. Find the probability that B is standing at the central position, given that A is standing at…2022
- A box has 4 green, 8 blue and 3 red pens. A student picks up a pen at random, checks its colour and replaces it in the box. He repeats this process 3…2025
- Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000…2026
- Let M and N be two events such that P(M)=0.6, P(N)=0.2 and P(M ∩ N)=0.5, then P(M^′ / N^′) is2025
- The probability distribution of a random variable X is: where k is some unknown constant. The probability that the random variable X takes the value…2024
CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.