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Question

# A signal which can be green or red with probability 45 and 15 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 34. If the signal received at station B is green, then the probability that the original signal was green is

A
35
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B
67
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C
2023
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D
920
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Solution

## The correct option is C 2023Let Event G= original signal is greenE1=A receives the signal correctE2=B receives the signal correctE= signal received by B is greenP(signal received by B is green) =P(GE1E2)+P(G¯¯¯¯E1¯¯¯¯E2)+P(¯¯¯¯GE1¯¯¯¯E2)+P(¯¯¯¯G ¯¯¯¯E1E2)=(45×34×34)+(45×14×14)+(15×34×14)+(15×14×34)P(E)=4680P(G/E)=(45×34×34)+(45×14×14)4680=2023

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