https://en.wikipedia.org/wiki/Bayes'_theorem

For example, if cancer is related to age, then, using Bayes’ theorem, a person’s age (prior knowledge) can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without prior knowledge of the person's age.

Bayes' theorem is stated mathematically as the following equation:[2]

 

where A and B are events and P(B) ≠ 0.

  • P(A) and P(B) are the probabilities of observing A and B without regard to each other.
  • P(A | B), a conditional probability, is the probability of observing event A given thatB is true.
  • P(B | A) is the probability of observing event B given that A is true.

Cancer at age 65

Let us assume that cancer and age are related.

the “base rate” or prior (i.e. before being informed about the particular case at hand) probability

　　　　1%    an individual’s probability of having cancer

　　　　0.2%  the probability of being 65 years old

the “current probability”, where “current” refers to the theorized situation upon finding out information about the particular case at hand

　　　　0.5% a person has cancer when they are 65 years old

calculate the probability of having cancer as a 65-year-old

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