subject: discrete mathss ain Ci aise money and externally Consucotion with gones

Question

subject: discrete mathss

ain Ci aise money and externally Consucotion with gones ne who successfully Confleteda Course in Discrete M¢thematics taght by "Dc.R Doran at Middlesex County Collage, the city then hires that pecson to design a lotery as tte mechanism to Taising the moneyThe prize Monies and their Coves poding Probabi ties are qive in the chart A)what amout of money ean you expect 4o uin ond what is a Fair pri0a to pay for a lotery ticket? should tle city change So they are guarayteed to gexsale reverve?

Explanation / Answer

(A) The sum of all probabilityes shall be equal to 1.

So here sum of all probabilites = 0.915

SO probability to win nothing = 1 - 0.915 = 0.085

Amount of money can you expect to win

E(X) = 5 * 0.32 + 10 * 0.25 + 20 * 0.16 + 50 * 0.10 + 100 * 0.06 + 500 * 0.02 + 1000 * 0.005 = $33.3

Lets say fair price is x

Fair price means on an average, you should not lose anything. So if you buy a ticket for Rs. xx, and win Rs. 5, then you gain net Rs. 5x5x. This gain should not be negative i.e. it has to be at least 0.

(5-x) * 0.32 + (10-x) * 0.25 + (20-x) * 0.16 + (50 - x) * 0.10 + (100 - x) * 0.06 + (500 -x) * 0.02 + (1000-x) * 0.005 + (0 -x) * 0.085 = 0

33.3 - x = 0

x = 33.3

so fair price of ticket woule be 33.33

(b) Here the city charge atleast $33.3 to gurantee revenue.

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