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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 transmitted to B. The probability each station receives correct signal is 34. If the signal received by B is green then the probability that 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 G=Original signal green A=A receives correct signal B=B receives correct signal E is the event that signal received by B is green. Hence required probablity is P(GE)=P(G∩E)P(E) Now, P(E)=P(GAB)+P(G¯A¯B)+P(¯GA¯B)+P(¯G¯AB) =45.34.34+45.14.14+15.34.14+15.14.34=4680 Also, P(G∩E)=P(GAB)+P(G¯A¯B)=4080 So, we have: P(GE)=P(G∩E)P(E)=4046=2023

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