Bayes formula and Information (II)

In fact, there is no complete statement of the problem in my previous post.

To apply Bayes formula, we need some another facts.

If the prior probability is the probability of been on the crime scene and murdered, and the likelihood is probability of been with the girl, than we should know if he was with girl, or not.

And another thing, that we need to apply the formula, is the knowledge that the information used to calculate likelihood is not that, used for the calculation of prior probability.

If we knew this, than the answer would be 2/3 * 0.1 = 1/15 (the formula is simpler in the case, due to zero probability of murder, if he was with girl).

If we could not rely on this, the answers can differ.

For example, the fact that could be used for the calculation of both probabilities could be simple:

If he was in bad mood, he would go on scene and kill any friend (with probability of 1/5), else he could meet girl (with probability of 1/3rd) or with probability of 7/15 he would go from the city in the opposite direction.

In this case probability would be 1/5.

And another extreme case is the following nature of events:

Boris could go only on the scene, always if he was with his girlfriend before and with 1/6th probability, if he was not with girlfriend.

The final probability in this case is 1/6 * 1/5 = 1/30 .

In real life we are having billions events that form another, more big events that could be analyzed with formulae. We have to had as much data as possible, and we should understand nature of events before making formal calculations.