I hope someone can help me with a probability problem I’ve been wondering about for several years.
Say you have a Lotto of 42 numbers, the Lotto people pick the winning ticket of 6 at random
(without replacement) A person can win with 6 matching numbers, or 5 or 4.
My question is, if you could buy a limited number of tickets, say 7 total, would it be to your advantage
to hit all 42 numbers when you buy the tickets (instead of picking them randomly)?
In other words, you would dump 42 numbered slips into a hat and chose seven tickets of six numbers
without replacement. By advantage, I mean do you increase your probability of winning any prize?
Put another way, if you picked randomly with replacement and by chance picked the same 6 numbers
all 7 times, your chance of winning any prize would be reduced for that set of numbers. Would it also
be reduced with only partially unique sets of numbers? For example, if you picked 1,2,3,4,5,6, and then
also 1,4,5,7,9,10, etc.
How would one go about figuring out the solution to this problem?
I tried it with a simpler version, using 6 numbers, chosing three, and making a match on 2 or 3, I figured the probability of winning any game but then I got stuck.
I feel that if you have an advantage with this method, it only would work with a lottery that allows
a range of matches for a winning ticket.
I hope my question makes sense.