1) After four rolls you are more likely to have rolled at least one seven.


2) Because each trial is equally likely to have a royal flush, and we will play until we get a royal flush, the most likely time to get the Royal flush is on the first trial, because the chance that the royal occurs then is 1 out of 40,000. The chance that it occurs on the second trial is slightly less, 1 minus the chance that it occured on the first trial times 1 out of 40,000. So if I have to get within 100 of the correct answer, I will choose the 100th trial.


Bob T.