A slip of paper is given to a person `A` who marks it either with a plus sign or a minus sign. The probability of his writing a plus sign is `1//3`. A passes the slip to `B`, who may either leave it alone or change the sign before passing it to `C`. Next `C` passes the slip to `D` after perhaps changing the sign. Finally `D` passes it to a refere after perhaps changing the sign. `B,C,D each change the sign with probability `2//3`.
If the refree observes a plus sign on the slip then the probability that A originally wrote a plus sign is