> But your test multiply those probabilities creating a much bigger probability for failure.
Minor nitpick: when probabilities multiply, they get smaller. Such is the nature of numbers in the range [0, 1].
Multiplication would happen when counting the probability of two (independent) events coinciding. What you're thinking about here is the probability of any one of several events occuring. That will be a (rather convoluted) sum, not a product.
We engineers can do convoluted sums, the assumption is that the events are independent and you multiply the probability of success (or 1-probability of failure).
Minor nitpick: when probabilities multiply, they get smaller. Such is the nature of numbers in the range [0, 1].
Multiplication would happen when counting the probability of two (independent) events coinciding. What you're thinking about here is the probability of any one of several events occuring. That will be a (rather convoluted) sum, not a product.