Powerball Mass Quickpick Odds The odds of picking the right powerball numbers for the jackpot are 1:292,201,338.  Right now, because the powerball has reached 1.4 billion dollars, many people are claiming that you could buy every possible combination and be guaranteed to profit.  Once you throw taxes and the chances of splitting the pot in, this is clearly not so... so please don't get into that.
Where my question comes in is, there would be no way humanly possible to buy all 292,201,338 combinations.  So someone proposed that you just buy 292,201,338 quick picks, which randomly pick numbers for you, and you would be virtually guaranteed the jackpot anyway.  I disagree and believe you would have closer to 2/3 chance of hitting the jackpot.
Which is correct, and what is the math behind these odds?
You shouldn't need to know the specifics of the lottery to answer this question, just that the odds of picking the right combination are x:y.  However, the specifics are:


*

*5 numbers are picked from a set of 1-69


*

*Numbers are not replaced into the set when picked

*Order does not matter


*1 number is picked from a separate set of 1-26

 A: Let $p$ be the probability that a random pick ticket wins. Then we want to know the probability that $n$ tickets picked randomly will have at least one winning ticket. This is the exact opposite of having $n$ tickets picked randomly having no winning tickets, which happens with probability $(1-p)^n$. Thus the answer we want is $1-(1-p)^n$. Plugging in your numbers, this probability is approximately .632, and you are correct.
For some more math on the powerball, note that the jackpot probabilities come from the number of possible number combinations. For the first part of the lottery ticket, you select 5 distinct number from 1-69 without regard to order and there are $\binom{69}{5}$ ways to do this. Multiply this by the 26 possibilities for the last number and you get the mystical 292201338 possibilities.
Additionally note that if it takes you 5 seconds to manually fill out a powerball ticket, it would take you 16910 days straight to fill out every single ticket combination. Thus it would take an army to effectively fill out these tickets, but that would mean sharing the winnings with all those fillers, and that would decrease the winnings even further.
A: Remember that the cost of a powerball ticket is $\$ 2.00$ so the $ 292$ million tickets cost would be $\$ 584$ million. Narrowing your profit x2. Then pay for your army of fillers and taxes taking close to half if you took the payoff all at once. Well now your at a loss in profit. God forbid there is more that one winner. Hell you'd go broke so don't even try. Because if you're not concerned about loosing all that money, then instead of throwing it away in the lottery just give it to me. I'm broke already so I could put it to good use and help out all my family and friends. Or not! 
