I am a bit confused and wonder if there is mistake in the bullet point here (C3_W1, section 2.2). It states that:

P(categorical x_k | C_i ) = \frac{\text{total number of samples in } X \text{ that have } x_k}{\text{ number of samples in } C_i}

But it possible that the number of samples in X that have x_k is greater than number of samples in C_i, which leads to a P > 1.

Is the correct division not:

\frac{\text{ number of samples in } C_i \text{ that have } x_k }{\text{ total number of samples in } C_i}

Apologies if I am misunderstanding.

Also, please could someone answer: Bayes Theorem - The Naive Bayes Model probability calculation - #10 by chris.favila