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The Vectorian Lounge => The Lounge => Topic started by: Triarius Fidelis on September 27, 2007, 11:31:24 pm

Title: theoretical probability question for mathematicians
Post by: Triarius Fidelis 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...
Title: Re: theoretical probability question for mathematicians
Post by: carsten on September 28, 2007, 03:57:38 am
The solution is 42

Carsten

... and thanx for the fish
Title: Re: theoretical probability question for mathematicians
Post by: exeterdad 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.
Title: Re: theoretical probability question for mathematicians
Post by: rbistolfi on September 28, 2007, 08:23:05 am
God, I missed you  :D
Title: Re: theoretical probability question for mathematicians
Post by: M0E-lnx 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
Title: Re: theoretical probability question for mathematicians
Post by: saulgoode 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

Title: Re: theoretical probability question for mathematicians
Post by: Vanger on September 28, 2007, 09:49:26 am
Use the common graphical representation via circles and everything should be clear.
Title: Re: theoretical probability question for mathematicians
Post by: MikeCindi 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...
Title: Re: theoretical probability question for mathematicians
Post by: Triarius Fidelis 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...  :-[