Bayes Theorem

Bayes' Theorem calculator computes the probability of event A occurring if event B is true.

INSTRUCTIONS: Enter the following:

• P(A) Probability of A being true independent of B
• P(B) Probability of B being true independent of A
• P(B|A) Probability of B being true if A has been observed (is true)

Bayes Theorem P(A|B): The calculator returns the probability as a real number.

The Math / Science

The formula for Bayes' Theorem is:

   `P(A|B) = (P(B|A)*P(A))/(P(B))`

where:

• P(A|B) = Probability of event A when event B is true
• P(B|A) = Probability of event B being true if A has been observed
• P(A) = Probability of event A independent of B
• P(B) = Probability of event B independent of A

Probabilities are expressed here as decimals between 0 and 1, where 0 means there is no chance of an occurrence and 1 implies a certainty of occurrence.  For example, an event with a 20% chance of occurrence has a probability of 0.2.  

Application

Baye's Theorem is helpful when considering test results, especially medical test results.  For example, you may have tested positive for a disease like Zika or HIV.  But there is a potential for a FALSE positive.  CLICK HERE for an insightful blog on how a false positive can be judged.