model {
for (i in 2:N) { # remove Bristol
y[i] ~ dbin(theta, n[i])
}
theta ~ dunif(0, 1)
# predicted number of deaths in centre 1 (Bristol)
y1.pred ~ dbin(theta, n[1])
P.bris <- step(y1.pred-y[1]-0.00001) + 0.5*equals(y1.pred, y[1])
}

Data:
list(N = 12, y=c(41,25,24,23,25,42,24,53,26,25,58,31),
n=c(143,187,323,122,164,405,239,482,195,177,581,301))

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   P.bris   0.0   0.0   1.0E-12   0.0   0.0   0.0   1001   10000
   y1.pred   16.05   3.81   0.04069   9.0   16.0   24.0   1001   10000