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

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

Infinity Learn · Accepted Answer

Even G $$-$$ original signal is $$greenE1$$ $$=$$ A receives the signal $$correctE2=$$ B receives the signal correctE $$-$$ Signal receive d by B is greenP $$(Signal$$ received by B is green $$)=PGE1E2+PGE$$¯$$1E$$¯$$2+PG$$¯$$E1E$$¯$$2+PG$$¯E¯$$1E2P(E)=465$$×$$16P(G/E)=40/5$$×$$1646/5$$×$$16=2023$$

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