Many states have a lottery and they post the odds of winning the grand prize and lower prizes;

An example would be that you need to pick six numbers ranging from 1 - 60

What are the odds of drawing three numbers? Four numbers? Five numbers? The grand prize?

Would this be considered independent or dependent? Why or why not?

Besides having a "Pick Six" lotto, there are other ones like a Pick-3 or Pick-4 where players choose a three or four digit number ranging from 0 - 9 and winning the straight prize requires the player to match their number exactly as drawn? What are the odds of winning those prizes?

Would this be considered independent or dependent? Why or why not?

Based off of your knowledge of probability, do "lucky numbers" exist? Why or why not?