For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit...

For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 3 systems detects theft with a probability of 0.84 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 3 systems will detect it. What is the probability that when a theft occurs, at least one of the 3 systems will detect it? Your answer should be rounded to 5 decimal places.

Expert Solution

the probability that when a theft occurs, at least one of the 3 systems will detect i = 1 - P(All 3 systems fail)

= 1 - (1 - 0.84)³

= 1 - 0.16³

= 1 - 0.004096

= 0.99590

So,

Answer is:

0.99590

orchestra answered 1 year ago

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