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Q.

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

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a

35

b

67

c

2023

d

920

answer is C.

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Detailed Solution

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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