OT - Disney bobbleheads mystery

[QuikSand]

Okay, there's a puzzle in here somewhere...

Recently, Mrs. Q was lured in by the clever folk at our local groceria, who were hawking various Kellogg's breakfast cereals for some bargain price. She ponied up for something like eight boxes of her favorite, Cocoa Krispies. (I do not object)

As it turns out, the box advertises that it contains a mini bobblehead doll, from a set of four Disney characters. ("Collect them all" - you know the drill) I took one look at the box, and reviewed the four characters available: Mickey Mouse, Donald Duck, Goofy, and Minnie Mouse.

Almost without hesitation, I looked at the eight cereal boxes and said "You know we're just going to get a bunch of Minnies."

. . .time passes. . .

Here we are now, most of the way through the boxes of cereal. And here is the sequence of bobblehead dolls that we have received from our investment:

Minnie
Mickey
Minnie
Minnie
Minnie
Minnie

Yes, that's right - five out of six Minnies.


So, without getting into obvious arithmetic questions... I have to just wonder. Why is it that (1) I quickly reached the cynical conclusion that we would "get screwed" by drawing the "lame" figure? And (2) I was right about it?

Does it somehow serve the Disney or Kellogg's people to give away more Minnies than Mickeys?

Or, is this just a strange coincidence? (and just what are the odds of getting 5 ouut of 6 Minnies, anyway?)


Maybe a related question would be:

-How many boxes would you have to open to have at least a 50% chance of getting a full set of all four characters if they are evenly distributed (25% chance of each character for any box)?

-Does this chance change if you alter the distributions, and make one or more more common than others?


Anyway... the mysteries of a good cereal box ought to be enough food for thought tonight.

[Easy Mac]

I'd say there is a good chance a large number of a particular character would go to a particular store. I doubt they had individual sorters who made sure to evenly distribute each bobblehead to each specific part of the country. Just the way it would logically come off the line.

[kcchief19]

I can't speak to the odds of distribution, but I believe your cynical belief that you would get a bunch of Minnies was inspired by reality.

As a former employee of the evil empire, er, the House of Mouse, I can confirm that Disney keeps a VERY careful eye on the collector market and does everything it can to create a collectibles market. By creating the collectibles market, Disney gets two things: (1) a market for products that would not be as popular if they were not purported to be "collectible"; and (2) the attention that comes along with the collectibles market. It's like free advertising.

Unless an item was a part of a series that was numbered and the distribution was even, it was (and I suppose still is) common for Disney to break up the distribution. And when free giveaways were the prize, even more so. Chances are you don't want a Minnie -- you likely want a Goofy, a Mickey or a Donald. By stuffing the boxes with Minnie, Disney and the Cocoa-Krispies people increase the likelihood that you will need to buy more boxes of cereal to get the bobblehead you are looking for.

Oh, and the answer is 1/3.

[Craptacular]

My wife is keeping sugar away from me.

[Travis]

Could also be that different cereal types are heavy loaded with a certain bobblehead type, so the Krispies might by Minnie heavy (heh), while other varieties could produce the same result with the other bobbleheads, encouraging people to try all of the different participating products, thereby hopefully getting you hooked on 4 or 5 different sugar products.

[cthomer5000]

Also, I'm sure the bobbleheads are put in the cereal boxes in succession, 1000 minnies, 1000 donalds, etc... then repeated. Generally when this stuff is then sent to Supermarkets, that Supermarket is likely to be working from 1 or maybe 2 shipments of product. Probably everybody who bought the cocoa krispies from that Supermarket has a ton of Minnies.

I think the same thing may even be true of "winners" on soda bottle cap contests. When I was in high school, there was a local deli who didn't get much traffic at all. For an entire week, when I'd pick up a Dr. Pepper after school, I was a winner of another free 20 oz. Dr. Pepper. I think I won something like 6 over the course of 8 purchases.

[TredWel]

-How many boxes would you have to open to have at least a 50% chance of getting a full set of all four characters if they are evenly distributed (25% chance of each character for any box)?

No work shown (if you're that interested in the work, PM me. I don't want to clog up the board with a bunch of combinatorics)

To find a complete set in 4 tries: 9.4%
To find a complete set in 5 tries: 23.4%
To find a complete set in 6 tries: 38.1%
To find a complete set in 7 tries: 51.3%

So, my answer is 7 boxes. If we changed the distribution so that it is uneven, we could still find the answer, and even respond in the general case, but the answers would require four times as much work, and it was fairly difficult using my aged knowledge of probability and the hypergeometric model in getting the results above as it is.

[korme]

Quik, what did those last 2 boxes turn out to have?

[AnalBumCover]

Originally posted by QuikSand
(and just what are the odds of getting 5 ouut of 6 Minnies, anyway?)

Given 25% probability of getting Minnie (M) vs. 75% probability of not, the probability [p(M)] of getting Minnie 5 out of 6 times is as follows:

p(M) = _____6!______ x (0.25)^5 x (0.75)^1
       (6-5)! x (5)!

p(M) = 6 x 0.00098 x 0.75 = 0.00045 = 0.045%

Someone please check my calculation. I think I'm using the correct formula.

[Rich1033]

Originally posted by QuikSand
[i]Almost without hesitation, I looked at the eight cereal boxes and said "You know we're just going to get a bunch of Minnies."

. . .time passes. . .

Here we are now, most of the way through the boxes of cereal.

I have no idea how you have not opened the rest of the them. After getting about 3 "Minnies" in a row I would have ripped open all remaining boxes.

I have to give it to you Quiksand, you are a much stronger man than I.

[QuikSand]

Just in case anyone's curious... this morning, I finished off the final box of Cocoa Krispies. The results of the last two boxes were...

::drum roll::

Minnie
Minnie

::rim shot::

Surprise!

[bosshogg23]

I have Donald Duck. Damn thing doesnt bobble a bit!

[albionmoonlight]

Sounds like someone needs to buy more cereal.

That couldn't have been their thinking, could it?

[Anthony]

but, excluding the fact that Mrs. Q got the cereal boxes at a bargain - how many boxes would the average person buying a normal amount of cereal have to buy in order to get all 4? how mnay items of a perishable good could Disney expect a consumer to buy for a collectible toy, once again exlcuding presence of a sale/bargain. i'm not sure that Disney has a conspiracy behind this, but i think they could manipulate the toys in a way so that out of 8 boxes you'd get results more long the lines of say 4 Minnies, 3 Donald's and a Mickey. Minnie is obviously the least desirable character and Mickey surely the higher in demand toy - but how does the company decide which out of Donald and Goofey is more valuable? and for a Bobble Head doll? not like the Mickey toy does anything more special than the other three? i find it funny that all things being equal, the Mickey toy will always - no matter what the product is - be considered more valuable.

i don't understand why i care so much. nevermind the above post.

[AnalBumCover]

Originally posted by QuikSand
Just in case anyone's curious... this morning, I finished off the final box of Cocoa Krispies.

Wait... In about a week, you finished off eight boxes of Cocoa Krispies? For this?

[QuikSand]

Originally posted by AnalBumCover
Wait... In about a week, you finished off eight boxes of Cocoa Krispies? For this?

Uhhh... I didn't put it quite that way... but...uhhh...

[Bee]

They produce more "Minnies" and less of the more popular characters to try to get people to buy more boxes of cereal to "complete the collection". It's a common marketing practice.

So you need to send the wife back to buy 8 more boxes.

[QuikSand]

Okay, so perhaps an update is in order. Mrs. Q has recently purchased three boxes of Frosted Flakes, which also feature mini bobbleheads. We're developing quite a collection, it seems.

The set is from Toy Story 2 - you can see the four characters at this site by running your mouse over Buzz Lightyear:

Toy Story 2 Bobbleheads

So, canyone care to guess what two figures we now have from this set? And to speculate what's in the third, as yet unopened, box?

[Bee]

I'd guess the red x.

[Easy Mac]

I'd say you have the little cow-boy, normally I'd say the alien, but he looks cool and people may want him b/c of that.

[Bee]

I'd say the little dog thing from the lion king. I don't see a cowboy Easy Mac?

[AnalBumCover]

Originally posted by Bee
I'd say the little dog thing from the lion king. I don't see a cowboy Easy Mac?

[Bee]

Ahh...I didn't notice QS had said it was the Toy STory one.

[QuikSand]

Thanks, AAC - I couldn't locate the direct link to the set.

[JeeberD]

I would say you're getting either the Cowgirl or the alien...

[kcchief19]

Yeah, I'm going to have to put my money on three Jessies. Yes, unfortunately, I know the name. The alien and Buzz are too popular, and you certainly aren't going to get your hands on a Woody. Not with Mrs. Q around at least.

[QuikSand]

The kewpie doll goes to kcchief19!

So, far we have...

Jessie
Jessie


And that's where my heavy wager goes for as-yet-unopened box #3, too.