Q39
1 markSection E

What are the possible amounts, the person can win?

Probability
Probability — Random Variable and Its Possible Values
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).

random variablesample spacepossible outcomesjackpot prize amountsprobability distribution

Marking Scheme

  • 11 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.

Analysis & 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 1+2+3=61+2+3=6 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.

Common Mistakes

  1. 1Omitting Rs 0 (no prize) as a possible outcome, since most tickets do not win anything.
  2. 2Listing prize tiers as ranges instead of the exact discrete amounts specified in the problem.

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.

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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.