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Question

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

A
3
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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 2023P(signal at B is green) (IV cases possible) P(original signal is green) × P(it is received correctly at A and B ) + P(original signal is red) × P(it is received wrongly at A but correctly at B) + P(original signal is red) × P(it is received wrongly at B but correctly at A) +P(original signal is green) × P(it is received wrongly at both A and B ) =45×(34)2+15×34.14.+15×34.14+45×(14)2=4680P(original signal is green given received at B is green) = 40/8046/80=2023Sum of Case 1 + Case IV

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