This should be an extremely simple math problem.

[soon2bepro]

Okay, here's the deal. Coca-cola launches a promotion where 10% of their $1 bottles come with a prize, a free $1 bottle.

Now, when you buy a $1 bottle, 10% of the time you'll get a free bottle, and 10% of those times you'll get another one, and so on.

What I'm trying to find out is the expectation in number of bottles every time you buy a $1 one.

Would 1.1111111111111111111111111111111111... expected bottles per $1 be correct?

[Silent A]

Assuming you include the bottle you actually bought, yes.

[Borodog]

Yes.

[Silent A]

[ QUOTE ]
Yes.

[/ QUOTE ]

I win.

[Borodog]

MY PONY TOO SLOW

[govman6767]

I used to work for coke. The caps with prizes on them come in large boxes that the employee's used to root through and take the small winners. like

1) Free 20 oz coke
2) Basketballs
3) CD's etc etc

So while your math book might say 10% chance of winning it's usually 1%.

Trust me.

Also on their bottling line any bottle that does not fill the whole way is removed uncapped (more winners for me) and dumped out.

There is no way 10% is a good # to go by.

You should inform your teacher of his phony math.

[Stu Pidasso]

About 20 years ago there was such a promotion in the northwest. All the caps had a tiny number printed on the side of them. I think it was number 3 that won you a free bottle. When I would buy a coke I would look at all the caps on all the bottles in the rack and pick a winner. I had cokes every day that summer but only paid for one of them.

Stu

[Silent A]

[ QUOTE ]
About 20 years ago there was such a promotion in the northwest. All the caps had a tiny number printed on the side of them. I think it was number 3 that won you a free bottle. When I would buy a coke I would look at all the caps on all the bottles in the rack and pick a winner. I had cokes every day that summer but only paid for one of them.

Stu

[/ QUOTE ]

When I was 12 there was a similar promotion involving 28g bags of chips. To see if you were a winner you had to look inside the plastic bag to see if it said "Free Bag". Because it was possible to see thorough the plastic the manufacturers tried to obfuscate the letters by putting cross-hatching in the appropriate area of the outside of the bag.

Why they didn't just put a solid black spot from the beginning I'll never know but it was relatively easy to see an "F" for a free bag. Most kids could get a free bag 75% of the time (1 in 10 or 12 were winners).

Small brag here. This was in Canada so the writing was in English and French. For a loser it would say "Sorry try again" on the first row, the same thing in French on the second row, and a bunch of Xs on the third row. For a winner, there was more to say so there would be French writing on the third row (rather than 'XXXXXXXXXXX'). What I figured out was that it was even easier to look for any curved writing on the bottom row. I had a 95% success rate with this. Virtually free chips for almost a year before they finally started putting a solid spot on the bags. And even then I could still find a winner about 2/3 of the time.

[jthegreat]

Mt. Dew did this when I was younger... you could look up through the bottle to the underside of the cap and if you knew what to look for, could get a free bottle every time. Sweet.