My Math Forum Bayes' Theorem

 Probability and Statistics Basic Probability and Statistics Math Forum

 January 20th, 2015, 12:51 PM #1 Newbie   Joined: Oct 2014 From: In the sea Posts: 15 Thanks: 1 Bayes' Theorem Hi, I've gotten a hang of conditional probability and mutually exclusive events but I always get stuck when trying to understand Bayes' theorem. I've read a couple good examples about false positives and false negatives during screening for example but still can't wrap my head around the formula : I don't understand how we jump from $\displaystyle P(A intersection B_j)=P(B_j intersection A)=P(B_j)P(A|B_j)$ to $\displaystyle P(B_j|A)=(P(B_j)P(A|B_j))/(P(A))$ Why are we dividing by P(A) ? Thanks, amphi Taken from here: Bayes' Theorem -- from Wolfram MathWorld
 January 20th, 2015, 01:19 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 688 Thanks: 243 It's a small piece of algebraic manipulation. $P(B_j|A) = \dfrac{P(B_j\cap A)}{P(A)}$ By the formula for conditional probability. From your given formula, we know that $P(B_j\cap A) = P(B_j)P(A|B_j)$ Substituting this into formula for $P(B_j|A)$ gives $P(B_j|A) = \dfrac{P(B_j)P(A|B_j)}{P(A)}$ As required. Thanks from amphinomos
 January 20th, 2015, 11:43 PM #3 Newbie   Joined: Oct 2014 From: In the sea Posts: 15 Thanks: 1 Thanks !

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