s. A new security system needs to be evaluated in the airport. The probability o
ID: 3041013 • Letter: S
Question
s. A new security system needs to be evaluated in the airport. The probability of a person being a security hazard is 2.5%. At the checkpoint, the security system denied a person without security problems 1.8% of the time. But the security system passed a person with security problems 1% of the time. (a) What is the probability that a person passes through the system? (b) What is the probability that a person who passes through the system is without any security problems? o) What is the probability that a random through the system and is without person passes any security problems?Explanation / Answer
a)probability that a person passes through the system
=P(not security hazard and passes through+ security hazard and passes through)
=(1-0.025)*(1-0.018)+0.025*0.01=0.9577
b) probability that a person is without security problems given passes through
=P(not security hazard and passes through)/P(passes through) =(1-0.025)*(1-0.018)/0.9577 =0.9997
c)
probability that a person passes through and without security problems) =(1-0.025)*(1-0.018) =0.95745
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