Question

For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems detects theft with a probability of .99 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the four systems will detect it. This probability is equal to:

Answer 1

Given is :

4 different alarm systems were installed in the vault.

Each of the four systems detects theft with a probability of .99 independently of the others.

For solving this question, we have to first find the probability that none works.

It will be given as:

As there is 0.01 probability that all four systems will fail to detect theft. As all are independent, we get probability as:
`(0.01)^(4)`

Now, we have to find the probability that at least one system detects the theft, it is given by:
`1 -(0.01)^(4)`