The casino La Bella Fortuna is for sale and you think you might want to buy it,

Question

The casino La Bella Fortuna is for sale and you think you might want to buy it, but you want
to know how much money you are going to make. All the present owner can tell you is that
the roulette game Red or Black is played about 1000 times a night, 365 days a year. Each
time it is played you have probability 19/37 of winning the player's bet of $10 and probability
18/37 of having to pay the player $10.
Explain in detail why the law of large numbers can be used to determine the income of the
casino(please describe why we can using the parameters given and also based off the situation), and determine how much it is (use the law of large numbersto solve) .

Explanation / Answer

The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes. So, in long run, very large iterations will come under law of large numbers and the given probability will come into effect.

So Expected profit of buying the casino = 1000 * 365 * (19/37 - 18/37) * 10 = $ 98648 per year

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