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, and determine how much it is.

Explanation / Answer

As per the given probability data:

The amount that can be won per game of play is = ( 19/37 - 18/37 )*10 = $(10/37)

The total games played in a year is: 1000*365 = 365000

So, the yearly profit for the casino is: 365000*(10/37) = $ 98648.64

So, over the long run, the casino is most likely to gain profits close to the above mentioned amount.

The yearly profit will not be exactly equal to the above value, but very close to the above value, considering the number of games played in a year.

This is what the law of large number says. When the number of games played become so large, then it is very very likely that the profits earned will be much closer to the predicted above.

Hope this helps !

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.