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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 4 · Set 1 · Q38
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in…
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has $\displaystyle 30$ red caps, Box II has $\displaystyle 20$ red and $\displaystyle 10$ green caps, and Box III has $\displaystyle 30$ green caps. The probability that a Box i is selected and a cap picked out is $\displaystyle \frac{\mathrm{i}}{6}$, where $\displaystyle \mathrm{i}=1,2,3$. Based on the above information, answer the following questions : A person selects a cap.
(i)
What is the probability that he selects a red cap ?
(ii)
If he selects a green cap, what is the probability that the cap has come from Box II ?
Marking-scheme solution
(i)
Let $\displaystyle B_{1}, B_{2}$ & $\displaystyle B_{3}$ be the event that box I, box II and box III selected respectively.
$\displaystyle P(B_{1})=\dfrac{1}{6}, P(B_{2})=\dfrac{2}{6}, P(B_{3})=\dfrac{3}{6}$
Now, P(selecting a red cap) $\displaystyle =\dfrac{1}{6} \times 1+\dfrac{2}{6} \times \dfrac{2}{3}+\dfrac{3}{6} \times 0=\dfrac{7}{18}$
(ii)
P(selecting a green cap) $\displaystyle =1-\dfrac{7}{18}=\dfrac{11}{18}$
Now, $\displaystyle P\left(\dfrac{B_{2}}{\text{Green cap}}\right)=\dfrac{\dfrac{2}{6} \times \dfrac{1}{3}}{\dfrac{11}{18}}=\dfrac{2}{11}$
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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.