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 0.88 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?

Question

Alexandria Conley

Mathematics

4 November, 16:10

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 0.88 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?

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Answers (1)

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Matthias Bowen · Answer 1

0.998272 (0.998 in 3sf)

Step-by-step explanation:

Probability (detects) = 0.88

Probability (doesn't detect) = 1 - 0.88 = 0.12

Total probability is always 1

Probability of atleast one detecting = 1 - probability (all not detecting)

= 1 - (0.12*0.12*0.12)

= 1 - 0.001728

= 0.998272