Can anyone explain in simple and clear terms.
Here is a really easy way to remember it. Think of the middle of a venn diagram with two possible events, A & B, which is the probability that both events happen: P(A^B).
You can figure this out two ways: either by figuring out what proportion of all of the chances of A happening does B also happen, which we call the probaility of B given A or P(B|A):
P(B|A) = P(A^B)/P(A)
or by doing the reverse, by figuring out the probability of A given B or P(B|A)
P(A|B)=P(A^B)/P(B)
Now, remember that P(A^B) is going to be the same no matter how we figure it out, so by solving for P(A^B) in both equations, we can combine the two:
P(A^B) = P(B|A)*P(A) [First equation]
P(A^B) = P(A|B)*P(B) [Second equation]
P(B|A)*P(A)=P(A|B)*P(B) [Combining the two]
So we can use this to find P(A|B) or P(B|A) (by solving for whichever one we need):
P(B|A) = (P(A|B)*P(B)) / P(A)
P(A|B) = (P(B|A)*P(A)) /P(B)
The very easiest way to remember this is that the top on both equaitions is just P(A^B) which is the probability of both A& B happening, so really all you are doing is taking the proportion of each circle in the venn diagram and figuring out how much of that circle is taken up by the area that overlaps with the other circle.
I wrote an article on Bayes’ Formula that may be of some help here: http://financialexamhelp123.com/bayes-formula/
Paraphrasing Derek Zoolander: “Listen to your friend S2000magician. He’s a cool dude.”
His explanation was exactly what I was going for, just clearer and more concise.
Thanks!
Drawing out a tree like in S200’s post is the way to go. You can’t make a mistake when you go that route. Easy points
Again with the 90% discount.
I must be slipping.