reliability

The probability of failure of $n$ components in series $P(\text{series failure})$, given we know the probability of failure for a single component $p_F$, is hard to compute (for the same reasons as in the birthday party problem).
But it’s easy to compute the opposite:

$$\begin{array}{rl}P(\text{series failure})& =1-P(\text{success})\\ & =1-(1-p_F{)}^n\end{array}$$

For $n$ components in parallel:

$$P(\text{failure})=p_F^n$$

When thinking about reliability / redundancy, it’s important to take into consideration whether your components are really independent.