Mathematics

Mathematics

Problem

Two independent security systems protect a vault. System A consists of two code-locks in series, requiring both to be correct (probability of correct entry =0.9= 0.9 each). System B consists of a biometric scanner (probability of success =0.95= 0.95). The vault opens if EITHER System A OR System B accepts the user. Assuming the user is authorized, calculate the probability the vault fails to open.

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