 DISCLAIMER: The information in this post is based on the assumption that all items without special percentages assigned in the box info have the same chance to appear when a box is opened. I cannot and will not take responsibility for any decision you make because of this post. The values have been calculated with software written on my own, so there is neither a guarantee that the code is errorfree nor that there are no typos in the post.
As the 5th Anniversary event slowly comes to an end now, this post tries to provide some help by showing the probability of getting desired items from a certain amount of boxes. It is part I of a series on the maths behind drop rates.
 Part I: Practical questions
 Part II: Extracting probabilities
 Part III: More than one box
 Part IV: Box inside a box
 Part V: The Asphalt 8 Box Calculator (tba)
 Part VI: All formulas in a nutshell (tba)
Update: Hidden rules
After opening 20 Expert Bundles in a row, I can say that there are definitely additional rules not mentionend in the box descriptions and infos. I didn't ever have one single box without either credits (18) or tokens (2). This changes the probability of "currency" to 100 % and makes it impossible to get 3 engines from one box. I have adapted the following table accordingly. The tokens/credits ratio given in the box info (2.5 % / 22.5 % of 4 items) is consistent with the real ratio of 2/18 in my boxes (10 % / 90 % of 2 items).
When I bought a Specialist Bundle, however, I had neither credits nor tokens in it, so the hidden rule only applies to Expert Bundles.
Overview
If you're not interested in the explanations, here's the overview of all items with their real probability (drop rate) in the "P" columns. Please note that the probabilities of all items counting as "Pro Kit Boxes" are assumed as equal.
How many coins can I earn?
 Quests: There are 30 quests with three levels rewarding 15, 25 and 35. If you accomplish all quests you get a bonus reward of 750, so the total number of coins you can get from quests is 3,000.
 Ads: Watching ads for 10 days (3 ads per day, average of 27.5 per ad) grants additional 825.
 On track: As some quests require a huge amount of finished races, it is also possible to collect about 100 per day automatically on tracks when playing races, which would result in 1,000.
We'll take this total of 4,825 as a base for further calculations.
Can I build an Audi R8 etron SE with those coins?
No.
 First: The car needs 150 blueprints to be assembled. For 4,825 you can buy 13 Expert Bundles with each box granting 1 to 7 blueprints. Even if you get 7 blueprints from every single box, you'll need 22 instead of 13 boxes which cost 7,700.
 Second: The chance of getting 7 blueprints from an Expert Bundle is $ \tfrac{1}{7} $ = 14.29 %. However, the chance of getting 7 blueprints 22 times in a row is $ \tfrac{1}{7^{22}} = \tfrac{1}{3,909,821,048,582,988,049} $. This is 1 out of 3.9 quintillions.
If you think of buying coins for real money: Don't. The expected (average) number of blueprints in an Expert Bundle is
 $ 1 \cdot \tfrac{1}{7} + 2 \cdot \tfrac{1}{7} + 3 \cdot \tfrac{1}{7} + 4 \cdot \tfrac{1}{7} + 5 \cdot \tfrac{1}{7} + 6 \cdot \tfrac{1}{7} + 7 \cdot \tfrac{1}{7} = 4. $
So you'd need 38 boxes which cost 13,300—and you can't be sure that this is enough because you can still get less than 4 blueprints per box.
Can I build a MercedesBenz SLK 55 AMG SE with those coins?
No.
The car needs 18 blueprints to be assembled. For 4,825 you can buy 32 Specialist Bundles with each box having a 10 % chance to contain 1 blueprint.
Your chance of getting at least 18 blueprints from 32 boxes is
 $ 1.17\times10^{8} $ or $ 0.0000000117 % $.
Here are some other probabilities for your information:


Can I build a BMW M2 SE with those coins?
Yes.
The car needs 70 blueprints to be assembled. For 4,825 you can buy 64 Novice Bundles that already contain 64 guaranteed blueprints for the car.
As the chance to get a second blueprint from a Novice Bundle is 75 %, it is almost certain that you get more than enough blueprints to assemble the car.
The table shows your chances of getting 6 additional blueprints from various amounts of boxes:
Boxes  P 

8  67.85 % 
9  83.43 % 
10  92.19 % 
12  98.57 % 
15  99.92 % 
Other probabilities
Each box is calculated with the abovementioned 4,825.
Expert Bundle
What you can expect from 13 boxes:
Specialist Bundle
What you can expect from 32 boxes:
Item  Amount  P  Amount  P  Amount  P 

Rare/Motorcycle Engine, MidTech  1  90.33 %  2  66.89 %  3  39.38 % 
Tokens  40  28.87 %  80  2.10 %  120  0.06 % 
Credits  12,500  89.74 %  25,000  19.45 %  37,500  0.30 % 
Novice Bundle
What you can expect from 64 boxes:
Item  Amount  P  Amount  P  Amount  P 

Common Engine  1  90.24 %  2  67.11 %  3  40.13 % 
How can I calculate this myself?
The maths behind this is quite complex and has to handle large numbers, so I wrote a few functions that do the work for me. I'll explain the mathematical background in my next posts and share the code with you.
It would have taken too much time to write all this down, and as the 5th Anniversary event ends soon, I wanted to share the results first.