[lucianbr]

While these are reasonable approaches, I do not think they live up to the mathematical meaning of "independent", and so invalidate the chances calculation.

Your two teams might well both use in some place in the system the same hardware or software component. This will make the probability of failure between the systems not be completely independent, for all that you paid two teams and they worked separately. Spent a lot of money, and the results will not be as expected. If they both use x86 Intel, and a Meltdown kind of thing happens, your "independent" systems will both fail from the same cause.

The transport analogy works great if you somehow imagine the transportation to be instantaneous, and only the decision to matter. But if you are already on a train and the train is delayed, you are not walking back home and taking the car. You have multiple options for transport, but you do not have a system built of independent components. You are not using the train and the car and the highway and the local roads all simultaneously.

I don't think you understand the requirements for the formula you wrote to be valid. Your examples do not fit, for all that they are reasonable and useful approaches. Your actual reliability with these approaches falls way below the multiple nines you think of.