A signal can be green, yellow, or red with respective probabilities 4/7, 2/7, and 1/7, is received by station A and transmitted to station B, and station B then transmits the signal to station C and, finally station D receives the signal from station C.
The probability of each station receiving the signal correctly is 5/7,and that if it's received incorrectly it is equally likely to be received as either of the two other colors.
Determine the probability that the original signal was green, given that the signal received by station D is green.

(In reply to solution by Charlie)

transMatrix =
[5/7, 1/7, 1/7]
[1/7, 5/7, 1/7]
[1/7, 1/7, 5/7]
tm4 =
[971/2401, 715/2401, 715/2401]
[715/2401, 971/2401, 715/2401]
[715/2401, 715/2401, 971/2401]
ans =
[971/2401, 715/2401, 715/2401]
ans =
[3884/16807, 2860/16807, 2860/16807]
ans =
[6029/16807, 5517/16807, 5261/16807]

Posted by Charlie on 2023-04-05 17:08:09