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        riddles >> putnam exam (pure math) >> Relative probability
        
(Message started by: howard roark on Jan 14^th, 2009, 5:10pm)

Title: Relative probability
Post by howard roark on Jan 14^th, 2009, 5:10pm

Can anyone say (define formally) what relative probability is ??

Tried on Internet, but din't find any concrete explanations...

Title: Re: Relative probability
Post by 1337b4k4 on Jan 14^th, 2009, 6:35pm

relative probability isn't really a formal term that's too useful for analysis as far as i can tell. relative probability seems to be what people call comparing the likelyhood of an event to the likelyhood of another event in some way.

Examples in use:

A is relatively more likely to occur than B.
A is 10% more likely to occur than B.
A is three times as likely to occur as B.
Americans are poor at estimating relative probabilities.

Its also possible that you're talking about the relative frequency interpretation of probability. This defines the probability of an event A (seeing heads when you flip a coin) as the expected long run ratio of occurrences of the event over total experiments (no of heads / no of times flipped) if you perform lots of experiments (coin flipping). You could say that the probability of rolling a '1' on a die is 1/6 if as you roll more and more die, the ratio of the number of times you see a '1' to the number of times you roll a die approaches 1/6. This notion of probability is what people cite when they experimentally find probabilities for events (What is the probability that a user who sees the wu forums will register?).
This is often how probability is first introduced to people, but it fails to capture the notions of probability in statements like "There is a 30% chance of rain on Apr 1,2009" or "there is a 40% chance that your cough is caused by the flu" or "There is a 30% chance that the meteor will blow up over the eastern hemisphere." Even though many humans gain some kind of understanding from the sentences, the idea of ratio of successes over repeated experiments doesn't easily apply, and this is why the idea of relative frequency is considered just one possible interpretation of probability.