Statistics And Probability Question 96
Question: Abhay speaks the truth only 60%. Hasan rolls a die blindfolded and asks abhay to tell him if the outcome is a prime abhay says, YES what is the probability that he outcome is really prime?
Options:
A) 0.5
B) 0.75
C) 0.6
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] There are two cases when Abhay will say ?Yes?. Case (i) the number that come out is a prime and abhay is speaking truth, probability for this case is $ P(P)\times P(T) $ Here P (P) = Probability of getting a prime = 3/6 = ½ = 0.5 P (T) is probability that Abhay is speaking truth and P (T) = 0.6 So probability for this case is $ 0.5\times 0.6=0.3 $ . Case (ii) The number that come out is not a prime and Abhay is not speaking truth, probability for this case is $ P(P’)\times P(T’)=0.5\times 0.4=0.2 $ 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 0.3/0.5=0.6.
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