conditional probability

juantheron · 2011-12-14 05:07:04

If A and B are two events associated with a random experiment

then How can i Prove that

Bob · 2011-12-14 05:29:47

hi juantheron,

By P(A/B) do you mean the probability of A given that B has happened?

I was taught to write this P(A|B)

The diagram shows this formula proved.

Bob

juantheron · 2011-12-14 05:37:29

bob bundy i want some explanation for your figure

thanks

Bob · 2011-12-14 05:47:16

Oh OK.

And I thought a picture was worth a thousand words.

Stage 1 = B happens or not

Stage 2 = A happens or not

There are four branches:

Both A and B happen
B happens but not A
not B but A happens
not B and not A

If B has happened , we must follow the top branch.
If A then happens as well, that probability is the probability of A given B. That line is red on my diagram.

To go along one line and then along another you multiply the probabilities together.

So going along the top route is :

P( B has to happen) x P(A also happens given that B has happened = red line) = P( both A and B have happened)

which is usually written

Bob

juantheron · 2011-12-14 05:57:04

yes got it

thanks bob

Bob · 2011-12-14 05:59:24

You're welcome!

Bob

model · 2012-02-01 22:59:51

ohh cool Thanks Bob from me too .

model · 2012-02-05 19:39:49

Hy Bob,

I want to know any application of Bayes's theorem .
Could you please give me useful application . thanks

Bob · 2012-02-06 08:46:19

Google bayes theorem evidence court case

Bob

Math Is Fun Forum

#1 2011-12-14 05:07:04

conditional probability

#2 2011-12-14 05:29:47

Re: conditional probability

#3 2011-12-14 05:37:29

Re: conditional probability

#4 2011-12-14 05:47:16

Re: conditional probability

#5 2011-12-14 05:57:04

Re: conditional probability

#6 2011-12-14 05:59:24

Re: conditional probability

#7 2012-02-01 22:59:51

Re: conditional probability

#8 2012-02-05 19:39:49

Re: conditional probability

#9 2012-02-06 08:46:19

Re: conditional probability

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