For any problem involving conditional probabilities one of your greatest allies is

Bayes' Theorem. Bayes' Theorem says that for two events A and B, the probability of A given B is related to the probability of B given A in a specific way.

**Standard notation:**
probability of A given B is written \( \Pr(A \mid B) \)

probability of B is written \( \Pr(B) \)

**Bayes' Theorem:**
Using the notation above, Bayes' Theorem can be written: \[ \Pr(A \mid B) = \frac{\Pr(B \mid A)\times \Pr(A)}{\Pr(B)} \]Let's apply Bayes' Theorem to the

Monty Hall problem. If you recall, we're told that behind three doors there are two goats and one car, all randomly placed. We initially choose a door, and then Monty, who knows what's behind the doors, always shows us a goat behind one of the remaining doors. He can always do this as there are two goats; if we chose the car initially, Monty picks one of the two doors with a goat behind it at random.

Assume we pick Door 1 and then Monty sho…

It's mostly finished and is projected to find a total of about 16000-17000 9-squares, so the estimate was close.

ReplyDeleteFinal total - 16338 9-squares. Not a bad estimate given the necessary crudeness of the calculation.

ReplyDelete