Odds of BINGO? (or... is BINGO beatable?)

[fatdave]

I got some junkmail from the Sands about "High Stakes Bingo" (lol) and got to wondering about the actual odds of the game.

According to wikipedia: "Numbers 1 to 15 are assigned to the B column, 16 to 30 to the I column, 31 to 45 to the N column, 46 to 60 to the G column, and 61 to 75 to the O column"

Assuming the above, assuming a 5x5 board, and assuming it is played till somebody gets a BINGO... what are the odds of getting a Bingo?

You have to take into effect the fact that you can get a BINGO across, up-and-down, or diagonal (let's ignore postage stamp, four corners, etc)...

How many cards would you have to buy to guarantee a 100% chance of a BINGO?

Let's say there were a $10,000 Bingo Prize, and you could buy a 5x5 card for $1 a piece. Would it cost more than $10,000?