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 13. 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 referee after perhaps changing the sign. B, C, D each change the sign with probability 23. If the referee observes a plus sign on the slip then the probability that A originally wrote a plus sign is

A slip of paper is given to a person A who marks it either with a plus

1.	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 13. 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 referee after perhaps changing the sign. B, C, D each change the sign with probability 23. If the referee observes a plus sign on the slip then the probability that A originally wrote a plus sign is
Answer» 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 $\frac{1}{3}$ . 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 referee after perhaps changing the sign. B, C, D each change the sign with probability $\frac{2}{3}$ . If the referee observes a plus sign on the slip then the probability that A originally wrote a plus sign is