R Code for Discrete Probability Example 2

prob1.the <- (12/31)* (12/31)? # theoretical probability with replacement

result <- rep(0,10000)
for(i in 1:10000){# simulation with replacement
trial1 <- sample(1:31,size=2,replace=T)
if((trial1[1]<13)&(trial1[2]<13)) result[i] <- 1}
prob1.sim <- sum(result)/10000
prob1.sim

prob2.the <- (12/31)*(11/30)#theoretical probability without replacement
prob2.the

result <- rep(0,10000)#simulation without replacement
for(i in 1:10000){
trial2 <- sample(1:31,size=2,replace=F)
if((trial2[1]<13)&(trial2[2]<13)) result[i] <- 1}
prob2.sim <- sum(result)/10000
prob2.sim