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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

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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