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set.seed(1234)
N1 <- c(10^3,10^4,10^5,10^6,10^7)
results <- numeric(length(N1))

cnt <- 1

for (j in N1) {
  N <- j
  triangle_exists <- logical(N) #pre-allocation 
  for(i in 1:N) {
    x <- runif(1, 0,1)
    y <- runif(1, 0,1)
    a <- min(x,y)
    b <- max(x,y)
    cond1 <- a<0.5
    cond2 <- b>0.5
    cond3 <- (b-a)<0.5
    triangle_exists[i] <- (cond1) & (cond2) & (cond3)
  }
  
  results[cnt] <- mean(triangle_exists)
  cnt <- cnt + 1
}