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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 $\displaystyle P(A intersection B_j)=P(B_j intersection A)=P(B_j)P(AB_j)$ to $\displaystyle P(B_jA)=(P(B_j)P(AB_j))/(P(A))$ 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: 686 Thanks: 243 
It's a small piece of algebraic manipulation. $P(B_jA) = \dfrac{P(B_j\cap A)}{P(A)}$ By the formula for conditional probability. From your given formula, we know that $P(B_j\cap A) = P(B_j)P(AB_j)$ Substituting this into formula for $P(B_jA)$ gives $P(B_jA) = \dfrac{P(B_j)P(AB_j)}{P(A)}$ As required. 
January 20th, 2015, 11:43 PM  #3 
Newbie Joined: Oct 2014 From: In the sea Posts: 15 Thanks: 1 
Thanks !


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