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A signal which can be green or red with probability `4/5 and 1/5` respectively, is received by station A and then and 3 transmitted to station B. The probability of each station receiving the signal correctly is `3/4` If the signal received at station B is green, then the probability that the original signal was green is (a) `3/5` (b) `6/7` (d) `20/23` (d) `9/20` A. `(3)/(5)` B. `(6)/(7)` C. `(20)/(23)` D. `(9)/(20)` Select the correct answer from above options

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Correct Answer - C From the tree diagram, it follows that `P(B_(G))=(46)/(80)` `P(B_(G)|G)=(10)/(16)=(5)/(8)` `P(B_(G)nnG)=(5)/(8)xx(4)/(5)=(1)/(2)` `P(G|B_(G))=((1)/(2))/(P(B_(G)))=(1)/(2)xx(80)/(46)=(20)/(23)`

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