Choosing an appropriate hypothesis

[Agent Smith]

@Dale and @FactChecker I think the discussion we've had is adequate for my level. Thank you.

One last question. For Bayes' theorem given as $P(H|D) = \frac{P(H) \times P(D|H)}{P(D)}$, the Wikipage says that $P(D) \ne 0$ (division by $0$). But I noticed that since $P(\neg A) = 1 - P(A)$, if $P(D) = 0$, we know that $P(\neg D) = 1$. Can't we use this knowledge to solve the division by $0$ problem?

So we could do $P(H|\neg D) = \frac{P(H) \times P(\neg D|H)}{P(\neg D)} = \frac{P(H) \times P(\neg D|H)}{1} = P(H) \times P(\neg D|H)$

 

[Dale]

Can't we use this knowledge to solve the division by 0 problem?

How? I don’t see what knowing a different number would do for you here.

 

[Agent Smith]

How? I don’t see what knowing a different number would do for you here.

We can still test the probability of the hypothesis, but it looks as though posterior probability < prior probability because(?) $P(\neg D|H)$ is going to be low.