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A signal which can be green or red with probability fraction numerator 4 over denominator 5 end fraction and fraction numerator 1 over denominator 5 end fraction comma respectively, is received by station A and then transmitted to station 8 The probability of each station receiving the signal correctly is fraction numerator 3 over denominator 4 end fraction.1 f the signal received at staTtion8 is green, then the probability that the original signal was green is

  1. fraction numerator 3 over denominator 5 end fraction    
  2. fraction numerator 6 over denominator 7 end fraction    
  3. fraction numerator 20 over denominator 23 end fraction    
  4. fraction numerator 9 over denominator 20 end fraction    

The correct answer is: fraction numerator 20 over denominator 23 end fraction


    Event G equalsoriginal signal is green
    E subscript 1 end subscript equals A receives the signal correct
    E subscript 2 end subscript equals 8 receives the signal correct
    E equalssignal rreceived by 8 is green
    P(signal received by 8 is green)
    Error converting from MathML to accessible text.
    Error converting from MathML to accessible text.
    Error converting from MathML to accessible text.
    Error converting from MathML to accessible text.
    Error converting from MathML to accessible text.
    Error converting from MathML to accessible text.
    Therefore,
    Error converting from MathML to accessible text.
    Hence, the correct answer is option (c).

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