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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` (d) `20/23` (d) `9/20`

A

`3/5`

B

`6/7`

C

`20/23`

D

`9/20`

Text Solution

Verified by Experts

The correct Answer is:
C
Even G = original signal is green
`E_(1)=A` receives the signal correct
`E_(2)=B` receives the signal correct
E = Signal received by B is green
P (Signal received by B is green)
`=P(GE_(1)E_(2))+P(GbarE_(1)barE_(2))+P(barGE_(1)barE_(2))+P(barGbarE_(1)E_(2))`
`P(E)=(46)/(5xx16)`
`P(G//E)(40//5xx16)/(46//5xx16)=20/23 `
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Knowledge Check

  • A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then 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

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    `6/7`
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    `(20)/(23)`
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    `(9)/(20)`

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