probability of a sprinkler system

[Tascja]

I'm doing my probability assignment and I having some trouble understanding which formula I need to use to solve this question:

A particular automatic sprinkler system for high rise buildings, office buildings and hotels has two different types of activation devices on each sprinkler head. One type has a reliability of .91( the probability that it will activate the sprinkler when it should is .91). The other type, which operates independently of the first type, has a reliability of .87.

Suppose a serious fire starts near a sprinkler head.
a) What is the probability that the sprinkler head will be activated?
b) What is the probability that the sprinkler head will not be activated?
c) What is the probability that both activation devices will work properly?
d) What is the probability that only the device with reliability .91 will work properly?

 

[pka]

Suppose that the two activation devices are [A & B.
\(\displaystyle P(A) = .91\,\& \,P(B) = .87\)

For (a) you want \(\displaystyle P(A \cup B) = P(A) + P(B) - P(A)P(B)\).

For (b) \(\displaystyle 1 - P(A \cup B)\).

For (c) \(\displaystyle P(A)P(B)\)

For (d) \(\displaystyle P(A \cap B') = P(A)P(B')\).