On a certain kind of slot machine there are 10 different symbols that can appear

Question

On a certain kind of slot machine there are 10 different symbols that can appear in each of three windows. The machine pays off different amounts when either one, two, or three lemons appear. What should the payoff ratio for each of the three possibilities if the machine is honest and there is no cut for the house?

10 On a symbols of can ap there are 10 different symbols that can appear in each of windows. The machine pays off different amounts when either one, two, or three lemons appear. What should be the payoff ratio for each of the three possibil- ities if the machine is honest and there is no cut for the house?

Explanation / Answer

probabilty that 1 lemon comes out of 10 in only one window out of 3 =3*(one will receive lemon and other two does not) =3*(1/10*9/10*9/10) =243/1000

probabilty that 2 lemon comes out of 10 in only one window out of 3 =3*(two will receive lemons and 3rd not)

=3*(1/10*1/10*9/10) =27/1000

probabilty that 3 lemon comes out of 10 in only one window out of 3 =(three will receive lemons )

=(1/10*1/10*1/10) =1/1000

hence they have probabilty in the ratio of 243:27:1 for 1,2, 3 lemons

now let payoff for 3 lemons A, 2 lemons B and 3 lemons C

as their payoff should be inversely proportion to their probabilty

hence A:B:C=1:1/27:1/243 =243:9:1

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