QUESTION 15 Independent Events and Multiplication Principle fire alarm Assume a fire alarm is wired with three independent sensors. Each of these will be triggered in the presence of smoke with probability p = 0.9. The probability of each of these being triggered is independent. a) Find the probability that all of the sensors are triggered. b) Find the probability that none of the sensors are triggered. c) Find the probability that at least one of the sensors is triggered and that the alarm will go of

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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QUESTION 15
Independent Events and Multiplication Principle
fire alarm
Assume a fire alarm is wired with three independent sensors.
Each of these will be triggered in the presence of smoke with probability p = 0.9.
The probability of each of these being triggered is independent.
a) Find the probability that all of the sensors are triggered.
b) Find the probability that none of the sensors are triggered.
c) Find the probability that at least one of the sensors is triggered and that the alarm will go off.
Transcribed Image Text:QUESTION 15 Independent Events and Multiplication Principle fire alarm Assume a fire alarm is wired with three independent sensors. Each of these will be triggered in the presence of smoke with probability p = 0.9. The probability of each of these being triggered is independent. a) Find the probability that all of the sensors are triggered. b) Find the probability that none of the sensors are triggered. c) Find the probability that at least one of the sensors is triggered and that the alarm will go off.
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