In: Statistics and Probability
A fire alarm system inside an office building has two types of
activation devices, A and B, which operate independently.
Probability that device A is turned on in the case of a fire is
0.97.
Probability that device B is turned on in the case of a fire is
0.85.
When there is a fire, the fire alarm system is turned on when at
least one of two activation devices is turned on.
Probability that both devices are turned on in the case of a
fire is_____________
Probability that the fire alarm system is turned on in the case of
a fire is _____________
Probability that the fire alarm system is not turned on in the case
of a fire is ___________
Solution:
A fire alarm system inside an office building has two types of activation devices, A and B, which operate independently.
Probability that device A is turned on in the case of a fire is 0.97.
P( A is turned on) = 0.97
Probability that device B is turned on in the case of a fire is
0.85.
P ( B is turned on) = 0.85
Now,
(a) The probability that both devices are turned on in the case of a fire is given by,
P(both devices are turned on) = (0.97)(0.85) = 0.8245
So, The probability that both devices are turned on in the case of a fire = 0.8245
(b) Probability that the fire alarm system is turned on in the case of a fire is given by,
P(fire alarm system is turned on) = P( A is turned on and B is turned off) + P(A is turned off and B is turned on) + P(A is turned on and B is turned on)
P(fire alarm system is turned on) = (0.97)(1-0.85) + (1-0.97)(0.85) + (0.97)(0.85)
P(fire alarm system is turned on) = 0.1455 + 0.0255 + 0.8245 = 0.9955
(c) Probability that the fire alarm system is not turned on in the case of a fire is given by,
P( fire alarm system is not turned on) = 1 - P(fire alarm system is turned on)
P( fire alarm system is not turned on) = 1 - 0.9955 = 0.0045
P( fire alarm system is not turned on) = 0.0045
Answer is 100% correct.
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