VectorLinux

Please login or register.

Login with username, password and session length
Advanced search  

News:

Visit our home page for VL info. For support and documentation, visit the Vector Linux Knowledge Center or search the Knowledge Center and this Forum using the search box above.

Author Topic: theoretical probability question for mathematicians  (Read 2375 times)

Triarius Fidelis

  • Vecteloper
  • Vectorian
  • ****
  • Posts: 2399
  • Domine, exaudi vocem meam
    • my website
theoretical probability question for mathematicians
« on: September 27, 2007, 11:31:24 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, 06:01:33 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 ...
Re: theoretical probability question for mathematicians
« Reply #1 on: September 28, 2007, 03:57:38 am »

The solution is 42

Carsten

... and thanx for the fish
Logged
Tam exacte ut oportet, non ut licet!

exeterdad

  • Packager
  • Vectorian
  • ****
  • Posts: 2046
Re: theoretical probability question for mathematicians
« Reply #2 on: September 28, 2007, 05:09:32 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: 2301
Re: theoretical probability question for mathematicians
« Reply #3 on: September 28, 2007, 08:23:05 am »

God, I missed you  :D
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

  • Administrator
  • Vectorian
  • *****
  • Posts: 3217
Re: theoretical probability question for mathematicians
« Reply #4 on: September 28, 2007, 08:27:06 am »

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

I better leave it alone

saulgoode

  • Vectorite
  • ***
  • Posts: 340
Re: theoretical probability question for mathematicians
« Reply #5 on: September 28, 2007, 09:39:21 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, 09:46:40 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
Re: theoretical probability question for mathematicians
« Reply #6 on: September 28, 2007, 09:49:26 am »

Use the common graphical representation via circles and everything should be clear.
Logged
Running silent, running deep

MikeCindi

  • Tester
  • Vectorian
  • ****
  • Posts: 1073
Re: theoretical probability question for mathematicians
« Reply #7 on: September 28, 2007, 11:01:44 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, 11:04:34 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
    • my website
Re: theoretical probability question for mathematicians
« Reply #8 on: October 02, 2007, 06:02:14 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