 # Bayes' Theorem Part-3 -- Explanation

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# Bayes’ Theorem Part-3 – Explanation

Image Credit: (https://luminousmen.com/post/data-science-bayes-theorem)

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:

OR

Now, the second equation can be rewritten as:

Where:

• 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.