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Class 12 Probability · Long Answer3 Marksexpectation

Class 12 Maths · Probability · Long Answer #114

A lottery sells10000 tickets at ₹1 each. It awards one ₹3000 prize, one ₹2000 prize and three ₹500 prizes to distinct tickets. Buy one uniform ticket. Find the expected prize and net gain.

✅ Step-by-Step Solution

Final Answer: Expected prize=₹13/20=₹0.65; expected net gain=−₹7/20=−₹0.35
  1. Let Y be the gross prize: ₹3000 with probability1/10000, ₹2000 with1/10000, ₹500 with3/10000, otherwise0.
  2. E(Y)=(3000+2000+3·500)/10000=6500/10000=13/20=₹0.65.
  3. The net gain is G=Y−1 because the ticket costs ₹1. By linearity E(G)=E(Y)−1=13/20−1=−7/20.
  4. Thus the expected gross prize is ₹0.65 and the expected net gain is −₹0.35.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Let Y be the gross prize: ₹3000 with probability1/10000, ₹2000 with1/10000, ₹500 with3/10000, otherwise0.
  • [1 mark] E(Y)=(3000+2000+3·500)/10000=6500/10000=13/20=₹0.65.
  • [1 mark] The net gain is G=Y−1 because the ticket costs ₹1. By linearity E(G)=E(Y)−1=13/20−1=−7/20.
  • [0.5 marks] Thus the expected gross prize is ₹0.65 and the expected net gain is −₹0.35.

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