It is well known that the lizard people from Kraktar make up 1% of the earths po

Question

It is well known that the lizard people from Kraktar make up 1% of the earths population, living among us secretly and using their advanced technology to shield themselves from our detection. Recently CSIRO in conjunction with the NSA have developed a test to detect if an individual is in fact a lizard person. The probability that test indicates an individual is a lizard person given that they are a lizard person is 0.95 The probability that the test indicates an individual is a human given that they are human is 0.90. (a) What is the probability that an individual is a lizard person given the test says that they are? (b) What is the probability that an individual is a human given that the test says they are?" 22498299,Find two other pairs of polar coordinates for (3

Explanation / Answer

Let L is the event that randomly selected person is a lizard. Here we have

P(L) = 0.01

and R shows the event that person is a normal person so

P(R)= 1 - P(L) = 1 -0.01 = 0.99

Let P shows the event that test indicates person is lizard and N shows the event that person is human.

P(P| L) = 0.95, P(N|R) = 0.90

By complement rule we have

P(P|R) = 1 - P(N|R) = 0.10

P(N|L) = 1 - P(P|L) = 0.05

(a)

Here we need to find the probability P(L |P).

By Bayes theorem the required probability is

P(L|P) = [P(P|L) P(L) ] / [P(P|L) P(L) +P(P|R) P(R) ] = [ 0.95 * 0.01 ] / [0.95 *0.01 + 0.10 * 0.99 ] = 0.0876

(b)

Here we need to find the probability P(R|N).

By Bayes theorem the required probability is

P(R|N) = [P(N|R) P(R) ] / [P(N|R) P(R) +P(N|L) P(L) ] = [ 0.90 * 0.99 ] / [0.90 *0.99 + 0.05 * 0.01 ] = 0.9994

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