The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemort being alive??

Question

Dumbledore is worried if Voldemort is still alive because he noticed a suspicious mark on a hand.

If Voldemort dies, the mark continuous to exist with a 20% probability.

On the other hand, if Voldemort lives on, the mark will stay with 100% chance.

The prior odds were a hundred-to-one against Voldemort surviving. What is the probability of Voldemort being alive??

Answer 1

P(Voldemort is alive|spot) = P(Voldemort is alive and spot)/P(spot) =

P(spot|alive)P(alive)/(P(spot|alive)P(alive)+P(spot|dead)P(dead)) =

100%(1/101)/(100%(1/101)+20%(100/101)) =

1/101/(1/101+20/101)) =

1/101/(21/101) =

1/21