﻿

# Baysian updating

We know that Dogmeat won on three occassions on which it rained, and there were four rainy days in total.So Dogmeat's probability of winning, given that it is now raining, is 3 / 4, or 0.75, or 75%, however you like to write it.

On the other hand, if you use only the new information about the weather, and neglect the previous counts of wins and losses, you would perhaps back Dogmeat.To do this, we need to examine four possible situations: Dogmeat wins when it rains; Dogmeat wins when it doesn't rain; Dogmeat loses when it rains; Dogmeat loses when it doesn't rain.We know that Dogmeat achieved three of his five wins on rainy days, and it only rained once when he lost. Since there were twelve races, the number of times he lost on a sunny day must be 12 - (3 1 2), which is 6.This is because three of his previous five wins have been on rainy days.

You might estimate his probability of winning as 3 / 5, or 60%, on this basis.

However, to do this would be to ignore a crucial piece of information — that overall Dogmeat has won fewer races than Fleetfoot.