Sock-dresser search

You left your socks some­where in your room. You think there’s a 45 chance that they’re in your dresser, so you start look­ing through your dresser’s 8 draw­ers. After check­ing 6 draw­ers at ran­dom, you haven’t found your socks yet. What is the prob­a­bil­ity you will find your socks in the next drawer you check?

You’re en­couraged to solve the prob­lem your­self be­fore look­ing up the an­swer. The an­swer can be found in Belief re­vi­sion as prob­a­bil­ity elimi­na­tion.