CBSE 2026 · Region 1 · Set 1 · Q37 · 4 marks
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)What is the probability that the person wins atleast ₹ $\displaystyle 2,00,000$ ?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.
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)
What is the probability that the person wins atleast ₹ $\displaystyle 2,00,000$ ?
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
From CBSE’s own marking scheme for this paper.
(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)
Required probability $\displaystyle =\dfrac{3}{100000}$
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 $\displaystyle \dfrac{174997}{2500000000}$
ProbabilityIndependent EventsApplycase_studyeasy
More from Probability
- Assertion: Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at…2023 · asked 3×
- A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances…2025 · asked 3×
- Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung…2026 · asked 3×
- The probability distribution of a random variable X is: where k is some unknown constant. The probability…2024 · asked 3×
- Recent studies suggest that roughly 12 % of the world population is left handed. Depending upon the parents,…2023 · asked 3×
- Two balls are drawn at random from a bag containing 2 red balls and 3 blue balls, without replacement. Let…2022 · asked 3×
- Let X be a random variable which assumes values x 1, x 2, x 3, x 4 such that 2 P(X=x 1)=3 P(X=x 2)=P(X=x 3)=5…2022 · asked 3×
- The probability distribution of a random variable X is given below: (i) Find the value of k. (ii) Find P(1 ≤…2023 · asked 3×
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.