Statistics And Probability Question 18
Question: Abhay speaks the truth only 60%. Hasan rolls a dice blindfolded and asks abhay to tell him if the outcome is a ?Prime?. Abhay says, ?No?. What is the probability that the outcome is really ?Prime??
Options:
A) 0.5
B) 0.75
C) 0.6
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] There are two cases when Abhay will say? No? Case (i) the number that come out is a prime and Abhay is not speaking truth, probability for this case is $ P(P)\times P(T’). $ Here P (P) = probability of getting a prime =3/6=1/2=0.5 P (T) is probability that abhay is speaking truth and P (T) $ =0.6soP(T’)=0.4 $ So probability for this case is $ 0.5\times 0.4=0.2 $ Case (ii) the number that come out is not a prime and abhay is speaking truth, probability for this case is $ P(P’)\times P(T)=0.5\times 0.6=0.3 $ . So total probability for the given case is 0.3+0.2=0.5. New sample space is 0.5 and we have to find the probability of case (i) which is 0.2/0.5=0.4.
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