Pepsi, Apple and Probability

[Deetee]

ok, Pepsi is running a promotion where if the bottle cap has a message written under it you win a free song download from Apple. The funny part is if you tilt the bottle just right you could read the winning (or non-winning) message. The odds of getting a winning cap are one in three.

I bet that they lie about the odds.
In the UK a couple of years ago I tried just this same tactic with some softdrink offer which said there were "100 000 winning bottles".
I checked about 30 bottles in each of 3 different supermarkets and found no winners.

I doubt there were more than a few million bottles nationally, so concluded that the company lied about the number of possible winners (or as scribble suggested, someone got there first and took all the winning bottles)

 

[HarryKeogh]

Re: Re: Pepsi, Apple and Probability

I bet that they lie about the odds.
In the UK a couple of years ago I tried just this same tactic with some softdrink offer which said there were "100 000 winning bottles".
I checked about 30 bottles in each of 3 different supermarkets and found no winners.

I doubt there were more than a few million bottles nationally, so concluded that the company lied about the number of possible winners (or as scribble suggested, someone got there first and took all the winning bottles)

I doubt it. To redeem the free song you have to install Itunes so it's a good way for Apple to get people to put their software on their computer (and a percentage of them will start buying songs regularly)

 

[(S)]

Re: Re: Pepsi, Apple and Probability

I bet that they lie about the odds.
In the UK a couple of years ago I tried just this same tactic with some softdrink offer which said there were "100 000 winning bottles".
I checked about 30 bottles in each of 3 different supermarkets and found no winners.

I doubt there were more than a few million bottles nationally, so concluded that the company lied about the number of possible winners (or as scribble suggested, someone got there first and took all the winning bottles)

p = chance-of-not-winning-at-all
q = chance-of-not-winning-once
n = number of tries
p = q^n

So, p^(1/n) = q.

So, if you have a 0.5 chance of not winning after 30 tries [you should't be surprised not to win on a 50-50 shot], that indicates that you had a 0.977 chance of not winning on any particular shot. That in turn says you have a 0.023 chance of winning, or 1-in-50. 50 * 100,000 winners gives you 5 million total bottles.
Working the math backwards (or forwards) from 10 million total bottles, you have a 0.01 chance of winning on any particular go, or a 0.99 chance of losing. That gives you 0.74 chance of losing after 30 tries, which makes winning with 30 bottles a 1-in-4 shot.

Long story short, there were probably a 100k winners, and you shouldn't be too surprised at having not won.

 

[Deetee]

Re: Re: Re: Pepsi, Apple and Probability

That gives you 0.74 chance of losing after 30 tries, which makes winning with 30 bottles a 1-in-4 shot.

Long story short, there were probably a 100k winners, and you shouldn't be too surprised at having not won.

I guess.
Thanks. Nevertheless I checked about 3 times that number. I can't remember how many exactly, but at the time I felt I was extremely unlucky not to find at least one winner considering the number of "attempts" (even if I was cheating by not purchasing the product)

 

[slimshady2357]

Re: Re: Re: Pepsi, Apple and Probability

p = chance-of-not-winning-at-all
q = chance-of-not-winning-once
n = number of tries
p = q^n

So, p^(1/n) = q.

So, if you have a 0.5 chance of not winning after 30 tries [you should't be surprised not to win on a 50-50 shot], that indicates that you had a 0.977 chance of not winning on any particular shot. That in turn says you have a 0.023 chance of winning, or 1-in-50. 50 * 100,000 winners gives you 5 million total bottles.
Working the math backwards (or forwards) from 10 million total bottles, you have a 0.01 chance of winning on any particular go, or a 0.99 chance of losing. That gives you 0.74 chance of losing after 30 tries, which makes winning with 30 bottles a 1-in-4 shot.

Long story short, there were probably a 100k winners, and you shouldn't be too surprised at having not won.

Assume winning with 30 bottles is 25% chance, he said he did that three times.

Chances of not winning after checking 90 bottles would be (0.75)^3 = 42%

Therefore he still would have only had about 58% chance of winning after checking 90 bottles

Crappy contest, I want to WIN

Adam

 

[wipeout]

Is this like the two goats and the car all over again?

Because my brain swallowed itself trying to make sense of that one.

Rolfe.

Ah, the infamous "Monty Hall problem"... It's that there are only 3 doors which screws everybody up.

I tried to make it more intuitive for myself, so I increased the number of doors and that worked.

With 1000 doors to 999 goats and 1 car, a first choice, 998 doors to goats opened in one go, and then the offer to switch the final choice of the 2 remaining doors, it becomes obvious that the chances are the car was elsewhere to my first-round choice was 999/1000, and there is now only 1 door elsewhere, so switching makes a lot of sense.

In the equivalent with 3 doors to 2 goats and 1 car, the chances are the car was elsewhere to my first round choice was 2/3, but there's now only one door elsewhere, so again switching makes sense.

 

[Drooper]

I was never good at this so if someone could figure it out for me I'd appreciate it...

ok, Pepsi is running a promotion where if the bottle cap has a message written under it you win a free song download from Apple. The funny part is if you tilt the bottle just right you could read the winning (or non-winning) message. The odds of getting a winning cap are one in three.

the question: if I'm at the convenience store and tilt the first bottle and see that it's not a winner and I put it back and grab a second bottle (from among dozens of bottles) and pay for it (without checking the cap) what are the chances the second bottle is a winner? my guess is 1 in 2 but it's pretty much that...a guess. Can someone provide the correct answer along with the math behind it?

The odds are one in three,. because the events are indpendent.

 

[Drooper]

[pedant mode] If there are exactly 1/3 of each and you have eliminated one, even if there are millions haven't the odds shifted, albeit in a miniscule fashion, towards 1/2[/pedant mode]

If there are millions of bottles then you have made no MATERIAL difference to your odds of winning.

[mode=supreme pedant]given the vagiaries of production and distibution, never will exactly 33.33.....% of the bottles in circulation be "winners". [/mode]