Answer:
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:
Now, we have to find the probability that at least one system detects the theft, it is given by: