Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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