Championship/2018 McLaren X2/Maths

During the championship, players are also offered a purchasable Mini Box:
However, it is not recommended to buy Mini Boxes if a player is aiming at Custom Racing Engines. Assuming that the probabilities of Advanced Tech and Custom Racing Engines (both legendary) are equal and that there can be only 1 Custom Racing Engine per Mini Box, the chance of getting a Custom Racing Engine from a box is
: 17.67 \% : 2 = 8.835 \%.
Even if a player buys 10 Mini Boxes for a sum of , the chance of getting at least 1 Custom Racing Engine is only
: 
\begin{align}
 &\sum_{k = 1}^{10} 0.08835^k \cdot \left (1 - 0.08835 \right )^{10-k} \cdot \binom{10}{k}\\
\\
\\
 &= 60.34 \%.
\end{align}
The amount n of boxes needed to get at least 1 (one!) Custom Racing Engine with a probability of is
:n \geq \frac{\ln(1 - 0.9)}{\ln(1 - 0.08835)} = 24.89 > 24.
This means that a player would have to spend for 25 boxes to get 1 Custom Racing Engine with a certainty of .