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Mathematics · 2026 · 4 marks
CBSE 2026 · Region 1 · Set 1 · Q37
In an online jackpot, there is one first prize of ₹ 3,00,000, two second prizes of ₹ 2,00,000 each and three third prizes of ₹ 50,000 each. A total…
In an online jackpot, there is one first prize of ₹ $\displaystyle 3,00,000$, two second prizes of ₹ $\displaystyle 2,00,000$ each and three third prizes of ₹ $\displaystyle 50,000$ each.
A total of $\displaystyle 1,00,000$ jackpot tickets each costing ₹ $\displaystyle 100$ were sold there by raising a fund of ₹ $\displaystyle 1,00,00,000$. Rohan bought one ticket.
Based on given information, answer the following questions :
(i)
What are the possible amounts, the person can win?
(ii)
(a)
What is the probability that the person wins atleast ₹ $\displaystyle 2,00,000$ ?
OR
(b)
What is the probability that the person does not win any amount?
(iii)
In another jackpot, Rohan also bought a ticket having a prize money of ₹ $\displaystyle 5,00,000$. The chances of winning the jackpot are $\displaystyle 1$ in $\displaystyle 1,00,000$. Find the probability that on exactly one of tickets he wins the jackpot.
Official answer
(i)
The possible amounts are: ₹$\displaystyle 3,00,000$, ₹$\displaystyle 2,00,000$, ₹$\displaystyle 50,000$, or ₹$\displaystyle 0$ (no prize). (ii)(a) P(win at least ₹$\displaystyle 2,00,000$) = ($\displaystyle 1$+$\displaystyle 2$)/$\displaystyle 100,000$ = $\displaystyle 3$/$\displaystyle 100,000$ = $\displaystyle 3$/$\displaystyle 10$^5. (ii)(b) P(does not win any amount) = ($\displaystyle 100,000$ - $\displaystyle 1$ - $\displaystyle 2$ - $\displaystyle 3$)/$\displaystyle 100,000$ = $\displaystyle 99,994$/$\displaystyle 100,000$ = $\displaystyle 49,997$/$\displaystyle 50$,000.
Marking-scheme solution
(i)
₹ $\displaystyle 300000$, ₹ $\displaystyle 200000$, ₹ $\displaystyle 50000$
(ii)
(a)
Required probability $\displaystyle =\dfrac{3}{100000}$
OR
(b)
Required probability $\displaystyle =1-\dfrac{6}{100000}=\dfrac{99994}{100000}$ or $\displaystyle \dfrac{49997}{50000}$
(iii)
P (Exactly on one of the tickets Rohan wins the jackpot) $\displaystyle =$ P [(He wins first and he loses second) or (He loses first and wins second)]
$\displaystyle =\dfrac{6}{100000} \times \dfrac{99999}{100000}+\dfrac{99994}{100000} \times \dfrac{1}{100000}=\dfrac{699988}{10^{10}}$ or $\displaystyle \dfrac{174997}{2500000000}$
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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.