Question

You lose at cards. Suppose the chances that the other person was card counting, P, is 1/1000.

You lose at cards again. This time, the chances that this person was counting cards, B, is 1/100.

The chances of B and not P is let's suppose 1/4, as it involves very similar pathways, motives, skills, character etc.

What is the updated chance of P?

Is it a fallacy to not update your belief in P (the chances that they were originally card counting) assuming that card counting B would be linked to card counting P?

Answer 1

To update the chance of P, we need to use Bayes' theorem. Plugging in the given values, we find that the updated chance of P is 5.6 times more likely.

Step-by-step explanation:

To update the chance of P, we need to use Bayes' theorem. Let's denote P as the probability that the other person was card counting originally, and B as the probability that they are card counting now. We also have the probability of B and not P as 1/4. Bayes' theorem states:

P(P|B) = (P(B|P){ P(P)) / P(B)}

Plugging in the given values, we have:

P(P|B) = (1/100)x(1/1000) / (1/100)x(1/1000 + 1/4)

Simplifying, P(P|B) = 5.6 times more likely