On the 2004 TV show Battlestar Galactica , Cylons are genocidal robots who revol

Question

On the 2004 TV show Battlestar Galactica, Cylons are genocidal robots who revolted against their human masters, killing off most of humanity. Some Cylons can even mimic the look and behavior of real humans. Reliable intelligence indicates that of the 48,000 humans that managed to escape, 8 are actually Cylons in disguise. One character, the genius scientist Dr. Baltar, has developed a Cylon detector with 99% sensitivity and 98% specificity. To his horror, the first person Dr. Baltar tests gets a positive result. What is the probability that given this positive result, the person is in fact a Cylon?

Explanation / Answer

N=48000

P(person is cylons)=8/48000=0.000167

Sensitivity=P(test is positive/person is cylon)=0.99

Specificity=P(test is negative/person is not cylon)=0.98

P(person is cylon/test is positive)={P(test is positive/person is cylon)*P(person is cylon)}/{P(test is positive/person is cylon)*P(person is cylon)+ P(test is positive/person is not cylon)*P(person is not cylon)}

={0.99*0.000167}/{0.99*0.000167+(1-0.98)*(1-.000167)}

=0.000165/{0.000165+.999997}

=0.000165/1.00016166

=0.00016497

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.