Hi,

Wikipedia states Bayes theorem as:

In my A-level Statistics book, it states the following:

Using a single feature (F) in Bayes theorem, would it be logical to state the following?

$\displaystyle P(C|F) = \frac{P(C)P(F|C)}{P(F)}$

The book states that $\displaystyle P(F|C) = \frac{P(C \cap F)}{P(C)}$

Hence, in Bayes theorem one may say:

$\displaystyle P(C|F) = \frac{\frac{P(C)P(C \cap F)}{P(C)}}{P(F)}$

The P(C)s cancel out, hence one is left with:

$\displaystyle P(C|F) = \frac{P(C \cap F)}{P(F)}$

Is this correct, or have I made a crucial mistake?

Thanks in advance