A slip of paper is given to an individual A, who marks it with either a plus or a minus sign; the probability of his writing a plus sign is 0.35. 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 or keeping the sign unaltered). Finally, D passes the paper to an umpire. It is unknown if D altered the sign on the paper or kept it unchanged. The umpire observes a plus sign on the slip.
It is known that B, C and D are the only individuals who can alter a sign and the probability of a change is the same for each of them and independent with probability 0.65.
What is the probability that A originally wrote a plus sign?