Two Questions

1. How many times must you throw two dice before you are more likely than not to roll a seven?


2. Assume the chances of getting a Royal Flush on a poker machine is one in 40,000. You walk up to that machine just as someone is being paid for a Royal on it. You start playing from that point and refuse to quit until you hit. If you were to predict the EXACT number of plays you need to make to hit it, the prediction that would have the best chance of being right is what? (I happen to know the precise answer. Can you come within a hundred?)