A particular automatic sprinkler system for high-rise apartment buildings, office buildings and hotels has two different types of activation devices for each sprinkler head. One type has a reliability of .91 (i. e. 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 particular 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?