Question

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?

Answer 1

0.998272 (0.998 in 3sf)

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