DNA profiling (4)

To understand the prosecutor's fallacy, we need to understand conditional probability. Conditional probability is the probability of something given that a certain set of circumstances already exist. Simple example - I shuffle a pack of cards and turn over the top one. What's the probability that it's an Ace? Answer 4/52 (52 cards in the pack, and 4 of them are Aces). I now turn over the next card off the top. What's the probability that this card is an Ace? A moment's thought will tell you that this depends on (is conditional upon) what the first card was. There are only 51 cards it can be and, depending on whether the first card was an Ace or not, there are 3 or 4 Aces still in the pack, so the answer is 3/51 (if the first card was an Ace) or 4/51 (if it wasn't). In probability maths we write P(A│B) to mean - the probability of A given that B is so.
The prosecutor's fallacy involves confusing P(A│B) with P(B│A), and we'll look at that next time.