Could you please show me the workings leading up to the answer. Thank you. QUEST
ID: 3355857 • Letter: C
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: 0.9994Explanation / 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