a <- runif(1000, 8, 10) # A deliveries
b <- runif(1000, 9, 11) # B deliveries
# [1] 9.485513 8.665070 8.488481 8.840332 8.755384 9.448949 # A deliveries for example

prob <- sum(b < a)/1000
#[1] 0.112 # almost 1/8

plot(a, b)
polygon(c(9, 10, 10, 9),
        c(9, 9, 10, 9), density = 10, angle = 135)

se <- sqrt(prob * (1 - prob) / 1000)
#[1] 0.009972763

prob - 1.96*se
#[1] 0.09245338 lower bound
prob + 1.96*se
#[1] 0.1315466 upper bound