What are the possible amounts, the person can win?
What are the possible amounts, the person can win?
Official answer
The possible amounts Rohan can win are: Rs 0 (no prize), Rs 50,000 (third prize), Rs 2,00,000 (second prize), and Rs 3,00,000 (first prize).
Marking scheme
- 1.1 mark: correctly listing all four possible amounts — 0, 50,000, 2,00,000, and 3,00,000 (accept any consistent notation).
Hint
List every distinct prize value stated in the problem, plus the 'no prize' outcome of Rs 0.
Quick oral answer
The possible winning amounts are Rs 0, Rs 50,000, Rs 2,00,000, and Rs 3,00,000, corresponding to no prize, third prize, second prize, and first prize respectively.
Common mistakes
- 1.Omitting Rs 0 (no prize) as a possible outcome, since most tickets do not win anything.
- 2.Listing prize tiers as ranges instead of the exact discrete amounts specified in the problem.
Analysis and explanation
This step identifies the sample space of the random variable "amount won," which is the necessary first step before computing any probabilities in the next part.
Concept
- The jackpot has exactly three distinct non-zero prize amounts (Rs 3,00,000; Rs 2,00,000; Rs 50,000) and, since only tickets out of 1,00,000 win a prize, the overwhelming majority of tickets — including possibly Rohan's — win nothing, i.e., Rs 0.
Exam trap
- Students often forget to include Rs 0 as a possible outcome, listing only the three prize amounts and missing the "no win" case, which is actually the most probable outcome.
Interesting facts
This scenario is a real-world instance of a 'discrete random variable' with a finite sample space, exactly the structure used to define probability distributions in the NCERT Probability chapter.
Government and private lotteries worldwide are legally required to publish exactly this kind of prize-tier and probability breakdown for transparency.
Question details
Q39 of 44 questions
- Board
- CBSE
- Class
- Class 12
- Subject
- Mathematics
- Year
- 2026
- Section
- Section E
- Marks
- 1
- Chapter
- Probability
- Topic
- Probability — Random Variable and Its Possible Values
- Bloom's level
- understand
- Syllabus topic
- Unit 7: Probability — Random Variables (Case Study: Prize Amounts in a Jackpot Draw)
- Author
- CBSE
- Reviewed by
- Padhantu Academic Team
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Frequently asked questions
Why is Rs 0 included as a possible amount?
Because out of 1,00,000 tickets only 6 win a prize; the remaining 99,994 tickets win nothing, so Rs 0 is a valid and indeed the most likely outcome.