Conditional Probability & Bayes’ Theorem on Arshad Siddiqui

Conditional Probability

Thu, 12 Mar 2026 00:00:00 +0000

Conditional probability updates the probability of an event when new information is available.

It shows up whenever a question says:

Key takeaway: Conditional probability is always:

joint probability ÷ probability of the condition.

The condition must not be an impossible event.

Mon, 01 Jan 0001 00:00:00 +0000

Often we split the world into cases \( E_1,E_2,\dots,E_k \) that:

Then for any event \( A \) :

\[ P(A)=\sum_{i=1}^{k} P(A\mid E_i)\,P(E_i) \]

Tree intuition:

flowchart TD
 S[Start] --> E1[Case E1]
 S --> E2[Case E2]
 S --> E3[Case E3]
 E1 --> A1["A happens"]
 E2 --> A2["A happens"]
 E3 --> A3["A happens"]

Bayes’ Theorem is a mathematical formula used to determine the conditional probability of an event based on prior knowledge and new evidence.

Thu, 12 Mar 2026 00:00:00 +0000

Naïve Bayes is a probabilistic classifier.

It predicts a class label by computing: