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A signal which can be green or red with ...

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)`

C

`(20)/(23)`

D

`(9)/(20)`

Text Solution

Verified by Experts

The correct Answer is:
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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