Bayes teorem

This is bluntly copied from https://www.freecodecamp.org/news/bayes-rule-explained/ to keep the information locally

The equation itself is not too complex:

There are four parts:

• Posterior probability (updated probability after the evidence is considered)
• Prior probability (the probability before the evidence is considered)
• Likelihood (probability of the evidence, given the belief is true)
• Marginal probability (probability of the evidence, under any circumstance)

Worked example of Bayes' Rule

Here's a simple worked example.

Your neighbour is watching their favourite football (or soccer) team. You hear them cheering, and want to estimate the probability their team has scored.

Step 1 – write down the posterior probability of a goal, given cheering

Step 2 – estimate the prior probability of a goal as 2%

Step 3 – estimate the likelihood probability of cheering, given there's a goal as 90% (perhaps your neighbour won't celebrate if their team is losing badly)

Step 4 – estimate the marginal probability of cheering – this could be because:

• a goal has been scored (2% of the time, times 90% probability)
• or any other reason, such as the other team missing a penalty or having a player sent off (98% of the time, times perhaps 1% probability)

Now, piece everything together: