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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 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 what?

 Jun 10, 2020
 #1
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Let me attempt this:

 

Case 1: first green, then read correctly 2 times.

4/5 * 3/4 * 3/4 = 36/80

Case 2: First green, read wrong 2 times.

4/5 * 1/4 * 1/4 = 4/80

Case 3: First red, then read correctly at first tower, then read wrong at second.

1/5 * 3/4 * 1/4 = 3/80

Case 4: First red, then read wrong at first tower, then read correctly at second.

1/5 * 1/4 * 3/4 = 3/80

 

The total probability for when it is green is (36+4+3+3)/80 = 46/80.

Cases 1 and 2 are the only cases where the original signal is green, so it is (36+4)/80 = 40/80

(40/80)/(46/80) = 40/46 = 20/23

 Jun 11, 2020

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