Aparticular automatic sprinkler system has two different types of activation devices for each 3 sprinkler head. one type has a reliability of 0.9; that is, the probability that it will activate the sprinkler when it should is 0.9. the other type, which operates independently of the first type, has a reliability of 0.8. if either device is triggered, the sprinkler will activate. suppose a fire starts near a sprinkler head. what is the probability that the sprinkler head will be activated?

There is an 85% probability that the sprinkler head will be activated.

Step-by-step explanation:

We have these following probabilities:

50% of the first sprinkler being triggered

90% of the first sprinkler being reliable

50% of the second sprinkler being triggered

80% of the second sprinkler being reliable.

What is the probability that the sprinkler head will be activated?

is the probability of the first sprinkler being triggered and activated. So:

is the probability of the second sprinkler being triggered and activated. So:

There is an 85% probability that the sprinkler head will be activated.