Pre-calculus Research Paper Many people believe that winning at casinos is purely luck. But, if based on this logic, how do casinos stay in business? Is it merely luck, or is the gambling industry actually based on mathematics?
In order to understand how these methods work, one needs a basic understanding of the difference between combination and permutation. In everyday life, combination is like taking a test. Some people start from the front, the back, or right in the middle, the order the people start the test does not mean they will get different results. For permutations, order does matter. A good example would be opening a lock on your locker. The numbers must be inputted in a certain order. If the lock combination is 7-27-2, only those numbers, in that order will work. Since the cards …show more content…
Jill is trying to get a straight flush. A flush consists of all a combination of five cards with the same suit. The combination formula Jill will use is:
In this case, n is the total number of cards (52) and r is the selection of cards given to us (5). So it would be (52!)/[5!(52-5)!], reduced it would be (52!)/[(5!)(47!)]. So, by using this formula and plugging in the correct numbers, there is a possibility of 2,598,960 hands. However, Jill does not want just any random set of cards. Jill wants a flush; this is where probability comes into play.
Probability, according to Merriam-Webster Dictionary, is "the chance that something will happen." Jill wants to know the probability of getting a flush. Since thirteen cards in one suit and a player is dealt five cards, using the combination formula: (13!)/[5!(13-5)!] Jill can see that a flush can be attained 1287 ways. But, that number only applies to one suit. If Jill multiplies 1287 x 4, she can see that there are actually 5148 possible flushes.
By using these numbers and the probability formula, Jill can figure out how likely it is to get a flush. The probability formula
In order to understand how these methods work, one needs a basic understanding of the difference between combination and permutation. In everyday life, combination is like taking a test. Some people start from the front, the back, or right in the middle, the order the people start the test does not mean they will get different results. For permutations, order does matter. A good example would be opening a lock on your locker. The numbers must be inputted in a certain order. If the lock combination is 7-27-2, only those numbers, in that order will work. Since the cards …show more content…
Jill is trying to get a straight flush. A flush consists of all a combination of five cards with the same suit. The combination formula Jill will use is:
In this case, n is the total number of cards (52) and r is the selection of cards given to us (5). So it would be (52!)/[5!(52-5)!], reduced it would be (52!)/[(5!)(47!)]. So, by using this formula and plugging in the correct numbers, there is a possibility of 2,598,960 hands. However, Jill does not want just any random set of cards. Jill wants a flush; this is where probability comes into play.
Probability, according to Merriam-Webster Dictionary, is "the chance that something will happen." Jill wants to know the probability of getting a flush. Since thirteen cards in one suit and a player is dealt five cards, using the combination formula: (13!)/[5!(13-5)!] Jill can see that a flush can be attained 1287 ways. But, that number only applies to one suit. If Jill multiplies 1287 x 4, she can see that there are actually 5148 possible flushes.
By using these numbers and the probability formula, Jill can figure out how likely it is to get a flush. The probability formula