A signal which can be green or red with probability $$45$$ and $$15$$ respectively is received by the station A and Transmitted to B . The probability of each station receiving signal correctly is $$34$$ . If signal in received in B is green. The probability original signal was green is

Question

A signal which can be green or red with probability $$45$$ and $$15$$ respectively is received  by the station A and Transmitted to B . The probability of each station receiving signal  correctly is $$34$$ . If signal in received in B is green. The probability original signal was green is

Infinity Learn · Accepted Answer

$$G=$$ Original signal green. $$A=A$$ receive correct signal, $$B=B$$ receive signal correct. E is signal received by B is green. $$PGE=PG$$∩$$EPEPE=PGAB+PGA$$¯B¯$$+PG$$¯AB¯$$+PG$$¯A¯$$B=45.34.34+45.14.14+15.34.14+15.14.34=4680PG$$∩$$E=PGAB+PGA$$¯B¯$$=4080$$∴$$PGE=PG$$∩$$EPE=2023$$

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A signal which can be green or red with probability 45 and 15 respectively is received by the station A and Transmitted to B . The probability of each station receiving signal correctly is 34 . If signal in received in B is green. The probability original signal was green is

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