# Harry Potter at Ollivander's

https://arbital.com/p/8zf

by Vojta Kovarik Jan 31 2018 updated Jan 31 2018

A simple word problem on the application of Bayes rule.

Harry Potter went shopping for a magic-wand, only to find out that wand which fits him the most is a twin-wand of the evil Lord Voldemort. How worried should Harry be about a possibility of some sinister connection with Voldemort (as opposed to this just being a coincidence)?

We assume that:

• the shop has 15 000 wands on offer;
• for a typical wizard, any of them is equally likely to be the best fit;
• upon entering, the unsuspecting Harry puts the odds of any connection with Voldemort at 1 to 1 000 and
• Harry assumes that if any such connection existed, it would have a 10% chance of affecting the wand-choice.

(example stolen from J.K. Rowling and E. Yudkowsky)

The solution can be found by applying the Bayes' rule:

By the assumption, the prior odds are (1 : 1 000). The likelihood ratio is (10% : 1/15000), which puts the updated probability at (1 : 1000) (1/10 : 1/15000) = (1/10 : 1/15) = ( 3 : 2). Therefore, the probability of a sinister connectionâ€™â€™ with Voldemort is 60% and Harry should be pretty worried.