Wednesday, April 19, 2017

History of Probability

The word probability comes from the latin word probabilis, meaning generally approved. The use of the word mathematically began in the 18th century. Until then, the word chance was used in its place; thus, people referred to the probability theory as the Doctrine of Chances. Even though betting was practiced in the renaissance period, no theory was established that could be used to calculate odds of winning or losing. The fathers of mathematical probability can are most likely identified as Pierre de Fermat and Blaise Pascal, although there were other major contributors in the 17th century. In 1654, a gamblers dispute led these two French mathematicians to uncover the theory of probability. They were playing a game in which 2 die would be rolled 24 times and they would bet on whether a double-six would come up. After exchanging letters, they were able to uncover some of the fundamental laws of probability.

Probability is the empirical value used to represent the likelihood that an event will occur. The number usually lies between 0 (impossible) and 1 (certainty). The rules of probability are used to simplify the computations that determine the probability of an event from the known probabilities of other events. The rule of subtraction branches from the two properties of probability: the probability of an event is between 0 and 1; the sum of the probabilities should equal 1. This rule basically states that (if there are only two possible events) you can subtract 1 from a possibility for that event to acquire the possibility of the other event. The rule of multiplication is when you want to see when two events intersect, or when both events occur. This rule basically states that if you want to know the probability of two events occurring, you would multiply the probability of each independent event occurring. For example, if you have 3 pennies and 4 dimes, and you want to know the probability of drawing two dimes (without replacement). The probability choosing the first dime is 4/7 and the probability of the second dime is 3/6. To get the probability of both, you would multiply (4/7)x(3/6)=2/7. The rule of addition is implemented when you want to see the probability that either event will occur. Basically, one would add the probability that each event will occur minus the probability that both events occur (using the rule of multiplication. An example of a question that would utilize the rule of addition is “What is the probability that someone picks a daisy, sunflower, or both?” Intuitive judgment about probability is often wrong, so the laws of probability are necessary and guide one when deriving probabilities. 

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