Problem
Suppose you are playing a card game and you believe you have a 75% chance of winning. Your friend Alicia-your sole opponent-looks at her hand and sighs. You think that there is a 80% chance she sighs given you will win, and there is a 20% chance she sighs given that you will not win. Using our updating rule and the information given, what is the probability you will win? Express as a reduced fraction of the form n/m to get credit.