Finally, a good box!
2000 SP Authentic Future Watch: Aaron Murray /999, Jarvis Landry /999, Ka'Deem Carey /999.
Autograph #1: Darqueze Denard.
Rookie Patch Autograph: Josh Huff /550.
Autograph #2: Blake Bortles 2000 Future Watch /25!
There are 150,552 cards in the set. There are supposed to be 8 cards per box but most boxes have 10 or 11. Let's just choose 11. (The higher number actually works in Panini's favor.) Divide 150,552 by 11, and that means there are 13,686 boxes in the entire production.
There are 312 total OBJ and Teddy RPAs
Let's assume that none of the OBJs and Teddy RPAs will ever appear in the same box. Divide 312 OBJ/Teddy boxes by 13,686 total boxes, and that means there is a .0228 chance of hitting one of those cards in the very first box of NT opened.
Alternatively, there is a .9772 chance of NOT hitting one of those cards in the very first box of NT opened. Expressed as a fraction that's (13,686-312)/13,686 or 13,374/13,686.
As each box of NT is opened and a OBJ/Teddy isn't hit, then the probability of hitting one of those cards goes up ever so slightly.
Similarly, as each box is opened and one isn't hit, the probability of not hitting one in the next box goes down. Number-wise, it looks something like this...
(13,374/13,686) x (13,373/13,685) x (13,372/13,684) x etc. as each box is opened.
Now, let's assume that 500 cases have been broken by now which is probably a reasonable assumption. There are 4 boxes per case. So that's 2000 boxes opened. (2000 boxes would also represent around 15% of the production run) We need to do that above equation 2000 times.
What's the probability of opening 2000 boxes of NT and not hitting a OBJ or Teddy RPA?
Expressed as an equation it looks something like this:
(13,374! / 11,374!) / (13,686! / 11,686!)
None of the scientific calculators I could find could hand this calculation because the numbers are too big, but it should be pretty close to zero and I think we can show that another way.
When figuring out a probability and a past event influences a future event, it's called conditional probability. Our situation is conditional since once a card is pulled, it is removed from the available pool and not replaced.
But because our numbers are so big, we can actually treat this as the opposite of conditional probability (unconditional probability?).
As we found out earlier, the chances of a OBJ/Teddy RPA NOT being pulled from the very first box of NT is (13,686-312)/13,686 or .9772. Even if 2000 boxes were opened and a OBJ/Teddy RPA still hadn't been hit, then the probability of NOT hitting one in the next box opened would be (13,686-2,000-312)/(13,686-2,000) or (11,374/11,686) or .9733.
.9733 isn't too different from .9772, so we can treat this entire calculation as unconditional probability (probability with replacement).
So, if the probability of NOT hitting a OBJ/Teddy RPA is .9772, and 2000 boxes have been opened, then the probability of that happening is...
.9772^2000 which is 9.27^-21 or basically zero.
Even if we used a lower probability like .9733 and 2000 boxes were opened, then the probability is still 3.11^-24 or basically zero.
For comparison, even with a probability of .9733 and only 200 boxes being opened (50 cases), the probability of still not hitting a OBJ/Teddy RPA would be .00446 or about 0.446% chance of happening.