how to prove Bayes theorem?

Question

how to prove Bayes theorem? (Develop from conditional probability ) 2 criterias -Total of law is probability -multiplication rule Can someone show me the mathematical proof & steps for this please?

There's a perfectly good proof on Wikipedia. Are there steps there that you don't follow and would like more explanation on? — Nick Peterson, Dec 05 '18 at 16:16

score 3 · Answer 1 · answered Dec 05 '18 at 16:19

3

The conditional probability is defined as $$ P(A|B) = \frac{P(A\cap B)}{P(B)}, $$ hence $$ P(A|B) P(B) = P(B|A) P(A) . $$

answered Dec 05 '18 at 16:19

Federico

5,900

score 1 · Answer 2 · answered Dec 05 '18 at 16:18

1

Hints

Write $P(A \cap B)$ two different ways using conditional probability
these are therefore equal by Euclid's first axiom
manipulate into Bayes' theorem (assuming none of the probabilities are $0$)

answered Dec 05 '18 at 16:18

Henry

157,058

how to prove Bayes theorem?

2 Answers2