Bayes' Theorem Part-3 -- Explanation

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Part-1 Link:

Part-2 Link:

Bayes’ Theorem Part-3 – Explanation

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Above image we’ve two overlapped events A and B. It can be, for instance A — i buy wet today, B — it’ll be rainy today. In a method or another, many events are associated with one another , as in our example. Let’s calculate the probability of A as long as B has already happened.

Since B went on , the part which now matters for A is that the shaded part which is interestingly A ∩ B. So, the probability of A given B seems to be:

Therefore, we can write the formula for event B given A has already occurred by:


Now, the second equation can be rewritten as:


  • P(A|B) — the probability of event A occurring, given event B has occurred.
  • P(B|A) — the probability of event B occurring, given event A has occurred.
  • P(A) — the probability of event A.
  • P(B) — the probability of event B.