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How many possibilities does the slot machine work with. Let us assume that there are three cylinders on the machine each one with 12 figures displayed. Pulling the lever rolls all three and results in 3 figures displayed in a row. So the possibility of one figure showing up on one cylinder is 1/12 but the probability of three identical figures showing up on all three is 1/12 x 1/12 x 1/12 = 1/1728. The probability of two identical figures showing up in the three cyliners is 1/12 x 1/12 x 3 = 3/144, the multiplication by three is done to show the cumulative possibility that the 2 identical figures can show up in three different ways on the cylinders. Finally the possibility that we are going to get one particular figure on any one of the three cylinders is 1/12+1/12+1/12= 3/12. To keep track of the balance of luck on the machine can be done by counting each seperate outcome, with a large number of plays the counts have to even out, eg with the calculations above we know that one outcome with three identical figures is 1/1728 so if you pull the lever 1728 times you know you should get one set of triple 7's or triple cherries, you know that by pulling the lever 1728 times you should get at least 12 occurences where all three figures are identical. |
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