Could you please show me the workings leading up to the answer. Thank you. QUEST

Question

Could you please show me the workings leading up to the answer. Thank you.

QUESTION4 It is well known that the lizard people from Kraktar make up 1% of the earth's 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 The probability that the test indicates an individual is a human given that they are human a) What is the probability that an individual is a lizard person given the test says that they are? person is 0.95 is 0.90 Ans: 0.0876 (b) What is the probability that an individual is a human given that the test says they are? Ans: 0.9994

Explanation / Answer

let probability of lizard man =P(Lizard)=0.01

and that of being Human=P(Human)=0.99

probability that test results is lizard= P(test lizard) and that of Human =P(test Human)

a)

probability of test saying lizard person P(test Lizard)

=P(lizard)*P(test Lizard|Lizard)+P(Human)*P(lizard person|Human)

=0.01*0.95+0.99*(1-0.9)=0.1085

therefore probability that individual is a lizard person given test says they are =P(lizard|test Lizard)

=P(lizard)*P(test Lizard|Lizard)/P(test Lizard) =0.01*0.95/0.1085=0.0876

b)

probability that test says Human =P(test Human)

=P(lizard)*P(test Human|Lizard)+P(Human)*P(test Human|Human)

=0.01*(1-0.95)+0.99*0.90=0.8915

hence  probability that individual is a Human person given test says they are =P(Human|test Human)

=P(Human)*P(test Human|Human)/P(test Human)=0.99*0.9/0.8915=0.9994

please revert for any clarification

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