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Author Topic:   Feeling Cheeky, but have a probability question...
Peter
Member (Idle past 1478 days)
Posts: 2161
From: Cambridgeshire, UK.
Joined: 02-05-2002


Message 1 of 3 (88555)
02-25-2004 9:36 AM


Feel a bit cheeky for asking, but I'd appreciate some
opinions on a debate that has come up where I work.
If you know that something cannot happen, is it approriate
to say that it has a probability of zero, or is
probability an inapproriate concept in that situation.
Similarly for a probability of one.
Opinions sought (alhtough I have a view myself).

Replies to this message:
 Message 2 by helena, posted 02-25-2004 10:12 AM Peter has replied

  
helena 
Suspended Member (Idle past 5844 days)
Posts: 80
Joined: 03-27-2008


Message 2 of 3 (88573)
02-25-2004 10:12 AM
Reply to: Message 1 by Peter
02-25-2004 9:36 AM


I would say the following (a physicists perspective maybe):
Saying something cannot happen and assigning a probability of zero to that event are exactly identical. One might argue that it is pointless to do so but such a zero probability can have some merit. For example: In quantum mechanics you will express the probability for a system for going from state a to state b, which would read (in qm notation): P(a->b)=C*< a|H'|b >
where basically a and b are the functions describing states a and b and H' describes the way in which the system is being influenced. The construct <|> is just a short notation for a certain mathematical operation (taking the complex conjugate of a multiplied by the operator multiplied by b and integrating over R3 usually).
Such a probability can turn out to be exactly zero for two given states a and b (not approximately but exactly). This then basically tells you that your system will not change from a to b (or vice versa) for the stimulus provided (which is described by H'). So a probability of zero can make a lot of sense...

This message is a reply to:
 Message 1 by Peter, posted 02-25-2004 9:36 AM Peter has replied

Replies to this message:
 Message 3 by Peter, posted 02-26-2004 7:13 AM helena has not replied

  
Peter
Member (Idle past 1478 days)
Posts: 2161
From: Cambridgeshire, UK.
Joined: 02-05-2002


Message 3 of 3 (88764)
02-26-2004 7:13 AM
Reply to: Message 2 by helena
02-25-2004 10:12 AM


I can see that a result which produces a probability
of zero is useful.
I'm talking more about assigning a probability (or liklihood)
of zero (or one) to some event, rather than determining via
probabilites that something has zero probability.
Not sure that's at all clear, but...

This message is a reply to:
 Message 2 by helena, posted 02-25-2004 10:12 AM helena has not replied

  
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