Suppose that a satellite defense system is established in which four satellites acting independently have a 0.9 probability of detecting an incoming ballistic missile. What is the probability that at least one of the four satellites detects an incoming ballistic missile? Would you feel safe with such a system?
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Since the satellites act independently, the probability that a single satellite does not detect the missile is 1 - 0.9 = 0.1. Since there are four satellites, the probability that none of them detect the missile is 0.1^4 = 0.0001. Show more…
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