Question

Are your odds better of winning the lottery by playing two sets of numbers in the same draw or playing two sequential lotteries (your answer does not have to include a calculation of the odds)? Explain your answer.

Answer 1

It depends on the lottery.

In your lottery, all bills are unique. So, the odds are indeed doubling as others have pointed out, and if you buy all different tickets, you have a 100% winning chance (though the cost of buying all those tickets is far greater than the lottery prize).

Another lottery:

Suppose that there is a lottery where all tickets are thrown in an pool. There is only one prize. The ticket that is randomly selected gets the prize. There are already 50 tickets sold.

If you buy one ticket, then your chance of winning is 151151.

If you buy two tickets, then your chance of winning is 252<251=2?151252<251=2?151.

So your odds are improved, but not doubled.

I guess this is where the confusion on the internet is from.