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 90 % is


 * $$n \geq \frac{\ln(1 - 0.9)}{\ln(1 - 0.08835)} = 24.89.$$

This means that a player would have to spend for 25 boxes to get 1 Custom Racing Engine with a certainty of 90 %.