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dice and money game
A casino wants to launch a new game, In the game a player is asked to roll two dices and he gets away with the money equal to the sum of the dices outcome.
Player needs to buy the chance every time he plays, What should the casino charge such that it makes profit in the long run or does not have to bear any loss ?
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Ans: Casino should charge $7 in order to not loose in the long run.
There are a total of 26 possible combinations of two dice output, and each output is equally likely, We should get the average sum possible and charge higher then that.
Average Sum = ((6*6 + 21) + (6*5 + 21) + (6*4 + 21) + (6*3 + 21) + (6*2 + 21) + (6*1 + 21))/36;
here 21 is sum of 1+2+3+4+5+6.
= (6*21 + 6*21)/36 = 7
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7 is the right answer… Coz a person can get a money from 2 to 12, and avg of this two number is 7 by which they will not be in loss (apply probability).