So, my understanding is that Powerball has 6 numbers.
The first 5 you pick from 1 to 69.
The last number you pick from 1 to 26.
So the odds are 1:292.2 million (roughly) if you pick your own numbers.
But if you let the computer pick the numbers for you, aren’t you basically saying: what’s the probability of the same 6 numbers being picked twice by two independent random events (the machine that sold you the ticket and the actually lottery drawing), and hence you are doubling your odds to 1:584.4 million?
Hypothetically, I guess if you were able to buy every single combination out of the 6 numbers, it would cost you $292.2 million for all the tickets. And with the current jackpot at $550 million, you would come out ahead $257.8 million, if no one else picked the same number. But if someone else happens to pick the same number as you, than you would have to share the prize.
