Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

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

juantheron
Member
Registered: 2011-10-19
Posts: 312

conditional probability

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

then How can i Prove that 

Offline

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

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: conditional probability

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


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

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

juantheron
Member
Registered: 2011-10-19
Posts: 312

Re: conditional probability

bob bundy i want some explanation for your figure

thanks

Offline

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

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: conditional probability

Oh OK. 

And I thought a picture was worth a thousand words.  sad

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


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

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

juantheron
Member
Registered: 2011-10-19
Posts: 312

Re: conditional probability

yes got it

thanks bob

Offline

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

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: conditional probability

You're welcome!  smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

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

model
Member
Registered: 2011-08-10
Posts: 142

Re: conditional probability

ohh cool Thanks Bob from me too . smile


Maths is Doctor that make our life easy .. smile smile

https://www.facebook.com/groups/Maths.GIS/

Offline

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

model
Member
Registered: 2011-08-10
Posts: 142

Re: conditional probability

Hy Bob,

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


Maths is Doctor that make our life easy .. smile smile

https://www.facebook.com/groups/Maths.GIS/

Offline

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

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: conditional probability

Google bayes theorem evidence court case

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

Offline

Board footer

Powered by FluxBB