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In a lottery there are 200 prizes of Rs 5 ,20 prizes of Rs 25 and 5 prizes of Rs 100.Assuming 10000 prizes tickets are to be issued and sold what is the fair price to pay for ticket?

1)Rs 0.2 2)Rs 0.4  3)Rs 0.5 4)Rs 0.6
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Best answer
Here fair price means on an average, you should not lose anything.  So if you buy a ticket for Rs. $x$, and win Rs. 5, then you gain net Rs. $5-x$. This gain should not be negative i.e. it has to be at least 0.

You win net Rs. $5-x$ with probability $\frac{200}{10000}$, win Rs. $25-x$ with probability $\frac{20}{10000}$, win Rs. $100-x$ with probability $\frac{5}{10000}$, and win Rs. $-x$ with probability $\frac{9775}{10000}$.

Last case occurs when you don't win any ticket and lose your Rs. $x$.

Now net expected amount you win =

$0.02(5-x) + 0.002(25-x) + 0.0005(100-x) + 0.9775(-x) = 0$

Hence $x = 0.2$

So option (1) is correct.

1 comment

I don't understand that how the point comes Buy a ticket for rs. X  and win rs. 5 , then you gain net rs. 5-X . And how rs. -X with probability 9775/ 10000

Can you please explain this point ..
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