### Conditional Probability Simulation
### Bayesian Probability 

# lie detector

prev <- 0.50	# prevalence = P(L)

sens <- 0.80	# sensitivity = P(+|L)

spec <- .90		# specificity = 1 - P(+|L^c)

reps <- 10000

true.pos.test.pos <- 0	# counter for lie detector catching a truly lying person

test.pos <- 0		# counter for lie detector says person is lying

for(i in 1:reps){
	# simulate a person as lying or not
	lie <- 0
	if(runif(1) < prev){	
		lie <- 1
	}
	# if lying simulate if test positive or not
	if(lie == 1 ){
		if(runif(1) <= sens){
			test.pos <- test.pos + 1
			true.pos.test.pos <- true.pos.test.pos + 1
		}
	}
	# if not lying simulate if test positive or not
	else{
		if(runif(1) <= (1-spec)) test.pos <- test.pos + 1
	}

}

# simulated probability

true.pos.test.pos/test.pos