NIMCET 2019 — Mathematics PYQ

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Question

NIMCET 2019 — Mathematics PYQ

NIMCET | Mathematics | 2019

If a man purchases a raffle ticket, he can win a first prize of Rs. 5,000 or a second prize of Rs. 2,000with probabilities 0.001 and 0.003 respectively. What should be a fair price to pay for the ticket?

Choose the correct answer:

Explanation

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, $E_{(g ain)}$ = $E_{(w in)}$ - $E_{(l oss)}$ = 0 $5000 \times P_{(w in = 5000)}$ + 2000 $\times P_{(w in = 2000)}$ - F $\times P_{(w in = 0)}$ = 0
Substituting in probability values and moving E(loss) -
$\Rightarrow$ F $\times (1 - 0.001 - 0.003) = 5000 \times 0.001 + 2000 \times 0.001$
$\Rightarrow$ F $\times (0.996) = 11$ $\Rightarrow$ F $= \frac{11}{0.996} \approx 11$ Fair price of the raffle ticket will be approximately 11.