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If a man purchases a raffle ticket, he can win a first prize of Rs. 5,000 or a second prize of Rs. 2,000 with probabilities 0.001 and 0.003 respectively. What should be a fair price to pay for the ticket?
1. Rs. 11
2. Rs. 15
3. Rs. 2,000
4. None of these

1 Answer

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Best answer
Correct Answer - Option 1 : Rs. 11

CALCULATIONS:

Given that P(win = 5000) = 0.001 and  P(win = 2000) = 0.003

Let P(win = 0) = P(not winning either prize).
Fair price (F) is defined as the case where expected gain(E) = 0.
Then, E(gain) = E(win) − E(loss) = 0
5000 × P(win = 5000) + 2000 × P(win = 2000) − F × P(win = 0)=0
Substituting in probability values and moving E(loss) - 
\(\Rightarrow \) F × (1 − 0.001 − 0.003) = 5000 × 0.001 + 2000 × 0.001
\(\Rightarrow \) F × (0.996) = 11
\(\Rightarrow \) F \( = \frac{{11}}{{0.996}} \approx 11\)
Fair price of the raffle ticket will be approximately 11.

Therefore, option (1) is the correct answer. 

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