Romeo and Juliet plan to meet over coffee between 3 PM and 4 PM. Not known for punctuality, either is willing to wait 15 minutes for the other to show up. What is the probability they will have coffee together?
We will do a graphical solution followed by simulations.
The required probability is the chance of two people meeting inside the shaded area of the circle. It is estimated as 1 – chance of both not making it inside the region = 1 – (3/4)x(3/4) = (16-9)/16 = 7/16 = 0.437.
R Simulations
itr <- 1000000
time_band <- 15
romeo <- runif(itr, 0, 60)
juliet <- runif(itr, 0, 60)
mean(abs(romeo - juliet) <= time_band)0.437
