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Question

A signal which can be green or red with probability 23 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
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B
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C
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D
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Solution

The correct option is C
Even G = original signal is green
E1 = A receives the signal correct
E2 = B receives the signal correct
E = Signal received by B is green
P = (Signal received by B is green)
=P(GE1E2)+P(G¯E1¯E2)+P(¯GE1¯E2)+P(¯¯¯¯¯¯¯¯¯¯GE1E2)P(E)=465×16P(GE)=405×16465×16=2023

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