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Divide the number of events by the number of possible outcomes. After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes.
In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given observation. It was invented by Ray Solomonoff in the 1960s. It is used in inductive inference theory and analyses of algorithms.
A probabilistic algorithm A is an algorithm whose behavior is partly con- trolled by random events. The computation of the output y on input x de- pends on the outcome of a finite number of random experiments. In partic- ular, applying A to the same input x twice may yield two different outputs.
Probability is the Bedrock of Machine Learning. Classification models must predict a probability of class membership. Algorithms are designed using probability (e.g. Naive Bayes). Learning algorithms will make decisions using probability (e.g. information gain).
I have a probability problem, which I need to simulate in a reasonable amount of time. In simplified form, I have 30 unfair coins each with a different known probability. I then want to ask things like "what is the probability that exactly 12 will be heads?", or "what is the probability that AT LEAST 5 will be tails?".
I know basic probability theory, so I know I can enumerate all (30 choose x) possibilities, but that's not particularly scalable. The worst case (30 choose 15) has over 150 million combinations. Is there a better way to approach this problem from a computational standpoint?
Any help is greatly appreciated, thanks! :-)
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