# 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?

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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