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JEE Advanced2010MathematicsProbabilityActual

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 green is

Options

  1. A3 5
  2. B6 7
  3. C20 23
  4. D9 20

Correct answer

C. 20 23

Step-by-step solution

From the tree-diagram it follows that gathered P (B_G G )= 10 16 = 5 8 P (B_G G )= 5 8 4 5 = 1 2 P (G B_G )= 1 2 P (B_G ) = 1 2 80 46 = 20 23 gathered

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