Question

Suppose two equally good teams are competing against each other in rounds. and that each team has the following PMF for scoring runs in a round:

The number of Runs 0 1 2 3

P 0.6 0.25 0.13 0.02

If the game is tied at the end of the Ninth round, what is the probability that the game will last more than 17 rounds? Solve by simulation in R.

Note: Getting a good estimate of the probability of a rare event may require a large number of trials.

Answer 1

SOLUTION :

Note that the simulation will take some time to run since the number of simulations in 10 millions.

Output of the probability is 0.009773654

Run the code below in R:

rm(list = ls())
set.seed(1001)

nnMC <- 1e7

sim <- function(x){
game <- 0
flag <- TRUE
while(flag){
x <- runif(2)
if(all(x<0.6))
flag <- FALSE
if(all(x>0.6) & all(x<0.6+0.25))
flag <- FALSE
if(all(x>0.6+0.25) & all(x<0.60+0.25+0.13))
flag <- FALSE
if(all(x>0.6+0.25+0.13))
flag <- FALSE
game <- game + 1
}
return(game)
}
res <- numeric(nnMC)
for(i in 1:nnMC)
res[i] <- sim()

sum(res>17)/sum(res>9)