Chance operations & probability theory
From GenerativeArt
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| - | Example: What is the probability of flipping a coin and getting heads? | + | '''Example: What is the probability of flipping a coin and getting heads?''' |
Total number of states in the ensemble = 2 (heads and tails) | Total number of states in the ensemble = 2 (heads and tails) | ||
| - | Example: What is the probability of drawing an ace of spades from a shuffled deck of cards? | + | '''Example: What is the probability of drawing an ace of spades from a shuffled deck of cards?''' |
Total number of states in the ensemble = 52 (total number of cards in the deck) | Total number of states in the ensemble = 52 (total number of cards in the deck) | ||
| - | Example: What is the probability of drawing an ace from a shuffled deck of cards? | + | '''Example: What is the probability of drawing an ace from a shuffled deck of cards?''' |
Total number of states in the ensemble = 52 (total number of cards in the deck) | Total number of states in the ensemble = 52 (total number of cards in the deck) | ||
| - | Example: What is the probability of flipping a coin and getting 4 heads in a row? | + | '''Example: What is the probability of flipping a coin and getting 4 heads in a row?''' |
Probability of the individual event = .5 | Probability of the individual event = .5 | ||
| - | Example: What is the probability of drawing 4 aces from a shuffled deck of cards? | + | '''Example: What is the probability of drawing 4 aces from a shuffled deck of cards?''' |
For the first card - | For the first card - | ||
| - | <SPAN STYLE="font-size: larger;">Pinball Example</SPAN> | + | <SPAN STYLE="font-size: larger;"><u>Pinball Example</u></SPAN> |
In this example a ball is dropped on the top pin of a triangular arrangement of pins. The ball ends up exiting in one of several columns. The probability that a ball will end up in a given column is a function of the number of paths that lead to that column. | In this example a ball is dropped on the top pin of a triangular arrangement of pins. The ball ends up exiting in one of several columns. The probability that a ball will end up in a given column is a function of the number of paths that lead to that column. | ||
| - | <SPAN STYLE="font-size: larger;">Pascal's Triangle</SPAN> | + | <SPAN STYLE="font-size: larger;"><u>Pascal's Triangle</u></SPAN> |
This geometric arrangement of numbers was devised by Blaise Pascal to demonstrate and calculate the probability of a proposition that is the combination of binary events. To construct Pascal's Triangle each number is the sum of the 2 numbers in the line above. The resulting numbers can be viewed as the expected statistical distribution. For example, flipping 3 coins there is only one way to get all heads or all tails, but 3 ways to get 1 tail and 2 heads (THH, HTH, HHT), and 3 ways to get 1 head and 2 tails. | This geometric arrangement of numbers was devised by Blaise Pascal to demonstrate and calculate the probability of a proposition that is the combination of binary events. To construct Pascal's Triangle each number is the sum of the 2 numbers in the line above. The resulting numbers can be viewed as the expected statistical distribution. For example, flipping 3 coins there is only one way to get all heads or all tails, but 3 ways to get 1 tail and 2 heads (THH, HTH, HHT), and 3 ways to get 1 head and 2 tails. | ||
| - | <SPAN STYLE="font-size: larger;">Uniform Distributions </SPAN> | + | <SPAN STYLE="font-size: larger;"><u>Uniform Distributions</u></SPAN> |
| - | <SPAN STYLE="font-size: larger;">The Normal or Gaussian Distribution </SPAN> | + | <SPAN STYLE="font-size: larger;"><u>The Normal or Gaussian Distribution</u></SPAN> |
| - | <SPAN STYLE="font-size: larger;">The Law of Large Numbers </SPAN> | + | <SPAN STYLE="font-size: larger;"><u>The Law of Large Numbers</u></SPAN> |
