1.Who was Blaise Pascal and how did he help start the study of probability?
2.Who was Pierre de Fermat and how did he help start the study of probability?
3.What was the relationship between Blaise Pascal and Pierre de Fermat and what were they studying when they began writing about probability ?
4.What is the probability that a certain event is going to happen?What is the probability that a certain event is going to happen?
http://en.wikipedia.org/wiki/Blaise_Pascal
http://en.wikipedia.org/wiki/Pierre_de_Fermat
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1. Blaise Pascal was a 17th-century French mathematician, physicist, and philosopher. He made significant contributions to various fields, including probability theory. Pascal's interest in probability theory began with his work on gambling problems, specifically analyzing games involving chance.
To understand how Pascal helped start the study of probability, you can explore his famous work called "Traité du triangle arithmétique" (Treatise on the Arithmetical Triangle). In this treatise, he introduced Pascal's Triangle, a numerical arrangement that facilitates the calculation of probabilities and combinations. By using this triangle, Pascal was able to explore various aspects of probability theory, such as the probability of winning or losing in different gambling scenarios.
2. Pierre de Fermat was a 17th-century French lawyer and mathematician. He is known for his contributions to various fields, including number theory and calculus. Fermat's interest in probability theory emerged from his correspondence with Pascal, where they exchanged ideas and solved problems related to games of chance.
Fermat's work on probability began with his investigation of problems posed by gamblers, specifically involving dice games. He developed the concept of expected value, which helps determine the average outcome of a game or event. This idea paved the way for further study of probability and became a cornerstone in the field.
3. Blaise Pascal and Pierre de Fermat had a close relationship when it came to the study of probability. They communicated through letters, discussing their findings, solving problems, and exchanging ideas on the subject. Their collaboration in probability theory is primarily centered around analyzing gambling games and determining the likelihood of different outcomes.
Both Pascal and Fermat were inspired by the gambling culture of their time, where avid gamblers sought mathematical explanations to predict their chances of success. Through their writings, they laid the foundations of probability theory and introduced fundamental concepts, such as Pascal's Triangle and Fermat's expected value.
4. The probability that a certain event is going to happen is a measure of the likelihood of that event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.
To calculate the probability of an event, you need to know the total number of possible outcomes and the number of favorable outcomes. The probability can be found by dividing the number of favorable outcomes by the total number of outcomes.
For example, if you have a standard six-sided die and you want to find the probability of rolling a 3, there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6). Therefore, the probability is 1/6 or approximately 0.1667.
It's important to note that calculating probabilities can become more complex when dealing with more complicated events or when multiple events are involved. In such cases, formulas like the addition rule, multiplication rule, and conditional probability can be used to determine the probabilities.