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Can the probability of an event ever be a transcendental number?
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In general,prob.s are not rational no.s.MeJennifer said:So then is it true that probabilites are not represented as ratios of a given sample space?
MeJennifer said:I try to understand why a probability can be extended to be anything more than that of a rational number.
MeJennifer said:So then is it true that probabilites are not represented as ratios of a given sample space?
MeJennifer said:So then is it true that probabilites are not represented as ratios of a given sample space?
I try to understand why a probability can be extended to be anything more than that of a rational number.
That is a beauty!robert Ihnot said:MeJennifer: Can the probability of an event ever be a transcendental number?
There is a famous math problem from 1777, not long after Laplace in 1771 begain submitting papers on probability; this problem does fit the bill: Buffon's Needle Problem.
Here, we draw parallel lines on the floor, d apart, and drop a needle of length l on the floor. How likely is it that the needle will land on a line? For l=d, the needle being as long as the distance between the lines, the answer is 2/pi =.6366
http://mathworld.wolfram.com/BuffonsNeedleProblem.html
Yes, it is possible for the probability of an event to be a transcendental number. Transcendental numbers are numbers that cannot be expressed as a finite or repeating decimal, and they can arise in certain mathematical and scientific calculations.
The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. In some cases, these numbers can involve irrational or transcendental numbers, leading to a transcendental probability.
Yes, there are real-world examples of transcendental probabilities. For instance, in quantum mechanics, the probability of a particle being in a certain location can be expressed as a transcendental number. Another example is in statistical mechanics, where the probability of a molecule having a particular velocity can also be a transcendental number.
A rational or decimal probability is a number that can be expressed as a finite or repeating decimal, such as 0.5 or 0.3333. A transcendental probability, on the other hand, cannot be expressed in this way and is often represented using mathematical symbols, such as pi or e.
No, the probability of an event cannot be an imaginary number. Imaginary numbers are a type of complex number that involves the square root of -1 and are used in certain mathematical and scientific calculations. However, probabilities are always expressed as real numbers between 0 and 1.