A home has installed 4 security systems to detect attempted break-ins. What is the probability that at least one of the 4 security systems will detect it?
They operate independently, and each has a .40 probability of detecting a break-in.
They operate independently, and each has a .40 probability of detecting a break-in.
1 Answer
Explanation:
Probability of at least one system detecting a break-in
If each system has a probability of
then each system has a probability of
The first system will fail to detect a break-in
Of that
Therefore both of the first 2 systems will fail
Similarly the first 3 systems will fail
and all 4 systems will fail
Therefore at least one of the systems will succeed