A secret government agency has developed a scanner which determines whether a person is a terrorist. The scanner is fairly reliable; 95% of all scanned terrorists are identified as terrorists, and 95% of all upstanding citizens are identified as such. An informant tells the agency that exactly one passenger of 100 aboard an aeroplane in which you are seated is a terrorist. The police haul off the plane the first person for which the scanner tests positive. What is the probability that this person is a terrorist

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Omm2 Omm2 · Answer 1 · 2020-09-23T04:13:53+02:00

Answer:

The probability of a person is a terrorist is [tex]0.161.[/tex]

Step-by-step explanation:

Let,

[tex]A=[/tex] Your neighbor is a terrorist

[tex]B=[/tex] Your neighbor tested positive

Now we want to find the value of [tex]P(A|B)[/tex] where

[tex]P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^c)P(A^c)}[/tex]

where [tex]P(A)=\frac 1{100}=1-P(A^c), P(B|A)=0.95,[/tex]

[tex]P(B|A^c)=1-0.95=0.05[/tex]

Therefore, [tex]P(A|B)=\frac{\frac{0.95}{100}}{\frac{0.95}{100}+0.05\times \frac{99}{100}}[/tex]

[tex]=\frac{\frac{0.95}{100}}{\frac{0.95+0.05\times 99}{100}}=\frac{0.95}{0.95+4.95}[/tex]

[tex]=0.161[/tex]

Hence, the probability of a person is a terrorist is [tex]0.161.[/tex]