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I know that: $$P(c|o) = \frac{P(o|c) P(c)}{P(o)}$$

My question is why can't one calculate $P(c|o)$ directly and not use this formula?

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    What do you mean 'calculate it directly'? This formula is meant only to put the (typically unknown) posterior distribution, P(c | o) in this case, in terms of the (typically known) sampling distribution and prior distributions.2011-11-21

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