Two jars, one containing three red, five green, and two yellow balls, the other containing five red, one green, and four yellow balls, if a single ball is drawn from each jar, what is the probability that at least one is green?

brute-force-probability.R

n <- 2^16
sampleOut <- list()
# Put balls in the two jars.
jar1 <- c("red","red","red","green","green","green","green","green","yellow","yellow")
jar2 <- c("red","red","red","red","red","green","yellow","yellow","yellow","yellow")
# Do the following n times.
for(place in 1:n){  
  # Take a random ball from each of the two jars
  jar1Samp <- sample(jar1,1)
  jar2Samp <- sample(jar2,1)
  # If at least one of the balls is green, then isGreen is TRUE.
  # If not, then it is false.
  if (jar1Samp=="green" | jar2Samp=="green") isGreen=TRUE else isGreen=FALSE
  sampleOut[place] <- isGreen
}

length(sampleOut[sampleOut==TRUE])/n