Inside probability theory, conditional probability is a way to calculate and measure the probability of some event happening if another event has already occurred.

The Bayes’ Theorem is one way of calculating a probability of something occurring when you know probabilities of other things happening. 

The Bayes’ theorem is a mathematical formula that explains how to update current probabilities of an event happening based on a theory when given evidence of the potential occurrence. It is calculated from the principles of conditional probability, it can be used as a tool for reasoning what could happen after the changing probabilities of a large range of new circumstances that create belief updates.

Below is Bayes’ theorem formula expressed as a mathematical equation:

where  and  are events and .

  •  is a conditional probability: the likelihood of event  occurring given that  is true.
  •  is also a conditional probability: the likelihood of event occurring given that  is true.
  •  and  are the probabilities of observing  and  independently of each other; this is known as the marginal probability.

The Bayes Theorem can be used to calculate the probabilities of something happening in conditions where multiple other things are occurring. It is one mathematical model that can be used for backtesting in trading and investing. 

bayes theorem formula

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