Yes, the selection is done randomly. This means you might win the lottery even if you have only 1 ticket and you might never win the lottery even if you have 21 million tickets every week.
If you notice to list of winners, it is obvious that most of the winners are those who have big number of tickets. But I have seen some winners with lower than 100 tickets.
So, 1. you can have higher chance if you have more tickets. But your chance will be never 100% 2. Having only 1 ticket make you eligible for winning the lottery. But your chance would be very low.