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


You must roll the dice 4 times in order to be more likely than not to roll a 7, but only as calculated before you roll the dice once. If you roll the dice 4 times and still haven't gotten a 7 your probability is still 1/6 on the next roll, though you are still more likely than not to get a 7 on your next 4 rolls.