Statistics
Class 12

Conditional Probability

P(AB)=P(AB)P(B)P(A|B) = \frac{P(A \cap B)}{P(B)}
0.10.20.30.400.20.40.60.81
P(A|B) = P(A∩B) / P(B)

Adjust Variables

P(A∩B)
pAB =
0.010.5
P(B)
pB =
0.11

Probability of A given that B has occurred. Fundamental to Bayesian reasoning and machine learning.

Real-World Applications

Medical diagnosis — P(disease | positive test).

Spam filtering — P(spam | contains "free money").

Recommendation systems — P(buy | viewed similar item).

Weather — P(rain | cloudy).

Insurance — P(claim | young driver).

Marketing — P(purchase | saw ad).

Criminal justice — P(guilty | evidence).

Credit scoring — P(default | income level).

Quality control — P(defective | machine A).

Genetics — P(disease | gene present).

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