LogFAQs > #937649651

Cheese_Crackers posted...

teepan95 posted...

I thought the conditional probability was the probability before either event had occured, as opposed to the probability of G_2 occuring once G_1 has already occured. They're at different points along the time axis, so to speak

I'm not an expert though, so I'm willing to admit that I'm very probably wrong

That's more of a physical or philosophical point, because they're mathematically the same. A probability of 0.3, for example, doesn't really mean anything physically. The mathematical interpretation is that if you perform infinitely many identical and independent trials, 30% of them will give that result. But physically this is impossible. You might perform 100 trials but only 29 of them give that result. Does this mean the mathematical probability is wrong? No, and that's why the mathematical definition is separate.

But isn't the whole point of conditional probability that the condition changes the probability? E.g. in this case, the probability of G_2 given G_1 is different to G_2 AND G_1?

The former would be 'further' along the time axis, since G_1 has 'already occured'
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