A security system sets a false alarm with probability 0.1, independently between applications of the security system. What is the expected value of the total number of alarms that will be set before 3 false alarms are set?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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A security system sets a false alarm with probability 0.1, independently between applications of the security system. What is the expected value of the total number of alarms that will be set before 3 false alarms are set?

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Let us denote X=the number of false alarmsn=Total number of alarms p=probability of success= 0.1n=sample size=Total number of alarms =nExpected value of false alarms=E(X)=3

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