model {
q[1] <- 0.5; q[2] <- 0.5 # prior assumptions
r <- 8; n <- 8 # data
r ~ dbin(theta[pick], n) # likelihood
pick ~ dcat(q[])
theta[1] <- 0.5 # if random (assumption 1)
theta[2] ~ dunif(0.5, 0.55) # if psychic
psychic <- pick - 1 # 1 if psychic, 0 otherwise
}

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   psychic   0.6012   0.4896   0.001601   0.0   1.0   1.0   1   100000

[example-8_7_1-paul0]