VectorLinux
March 08, 2014, 11:53:11 pm
 News: Visit our home page for VL info. To search the old message board go to http://vectorlinux.com/forum1. The first VL forum is temporarily offline until we can find a host for it. Thanks for your patience. Now powered by KnowledgeDex.
 Pages: [1]
 Author Topic: theoretical probability question for mathematicians  (Read 1828 times)
Triarius Fidelis
Vecteloper
Vectorian

Posts: 2399

Domine, exaudi vocem meam

 « on: September 27, 2007, 10:31:24 pm »

I read that the probability that at least one of events A and B will occur in a trial is P(A + B) = P(A) + P(B) - P(AB), where A and B are not mutually exclusive events. That makes sense, because one would count the probabilities of A and B together, and then ignore event AB, because that counts instances of A and B twice, in the same way that the probability that at least one die of two will turn up six is 11/36, not 1/3.

That made sense intuitively, but I couldn't quite follow the proof because it mentioned things I never saw before. I noticed however, that the following relation also appears to be true (AC and BC are complementary events because latex2html is a dick.)

P(ACBC) + P(AB) + P(ACB) + P(ABC) = 1
P(AB) + P(ACB) + P(ABC) = 1 - P(ACBC)

and so

P(A + B) = 1 - P(ACBC)

I did it on some practice examples and it made sense, but what do I know...
 « Last Edit: October 02, 2007, 05:01:33 am by hanumizzle » Logged

"Leatherface, you BITCH! Ho Chi Minh, hah hah hah!"

Formerly known as "Epic Fail Guy" and "Döden" in recent months
carsten
Vectorite

Posts: 137

I know why birds sing ...

 « Reply #1 on: September 28, 2007, 02:57:38 am »

The solution is 42

Carsten

... and thanx for the fish
 Logged

Tam exacte ut oportet, non ut licet!
Packager
Vectorian

Posts: 2046

 « Reply #2 on: September 28, 2007, 04:09:32 am »

P(ACBC) + P(AB) + P(ACB) + P(ACB) = 1
P(AB) + P(ACB) + P(ACB) = 1 - P(ACBC)

and so

P(A + B) = 1 - P(ACBC)

Whaddid he say??    One of these days that brain of yours is going to blow up Hanu.
 Logged
rbistolfi
Packager
Vectorian

Posts: 2255

 « Reply #3 on: September 28, 2007, 07:23:05 am »

God, I missed you
 Logged

"There is a concept which corrupts and upsets all others. I refer not to Evil, whose limited realm is that of ethics; I refer to the infinite."
Jorge Luis Borges, Avatars of the Tortoise.

--
Jumalauta!!
M0E-lnx
Vectorian

Posts: 3134

 « Reply #4 on: September 28, 2007, 07:27:06 am »

WoW.....
My brains just overheated from just reading and trying to make sense of this thread....

I better leave it alone
 Logged

saulgoode
Vectorite

Posts: 340

 « Reply #5 on: September 28, 2007, 08:39:21 am »

Shouldn't the starting point for the complementary case be stated:

P(ACBC) + P(AB) + P(ACB) + P(ABC) = 1

 « Last Edit: September 28, 2007, 08:46:40 am by saulgoode » Logged

A complex system that works is invariably found to have evolved from a simple system that works.
Vanger
Packager
Vectorite

Posts: 118

 « Reply #6 on: September 28, 2007, 08:49:26 am »

Use the common graphical representation via circles and everything should be clear.
 Logged

Running silent, running deep
MikeCindi
Tester
Vectorian

Posts: 1068

 « Reply #7 on: September 28, 2007, 10:01:44 am »

Shouldn't the starting point for the complementary case be stated:

P(ACBC) + P(AB) + P(ACB) + P(ABC) = 1
That's correct...and I believe that the way Hanu worked his query is using this starting point versus his. Thus just a typo on his part. I'm not sure that I'm the one to comment on whether he got it right though...
 « Last Edit: September 28, 2007, 10:04:34 am by mikecindi » Logged

The plans of the diligent lead to profit...Pro. 21:5
VL64 7.1b3                                     RLU 486143
Triarius Fidelis
Vecteloper
Vectorian

Posts: 2399

Domine, exaudi vocem meam

 « Reply #8 on: October 02, 2007, 05:02:14 am »

Shouldn't the starting point for the complementary case be stated:

P(ACBC) + P(AB) + P(ACB) + P(ABC) = 1

Yes...
 Logged

"Leatherface, you BITCH! Ho Chi Minh, hah hah hah!"

Formerly known as "Epic Fail Guy" and "Döden" in recent months
 Pages: [1]