Question

At a particular blood bank, 45% of donors have type O blood. On a certain day, the blood bank needed 4 donors with type O blood and it took 12 donors to meet their quota. This surprised the director since it usually doesn’t take that many donors to find 4 with type O blood. Could this have occurred by random chance or were people with type O blood particularly stingy on that day? Design and conduct a simulation (do 10 runs) to estimate the probability it takes 12 or more donors to get 4 with type O blood. On average, how many donors does it take to get 4 with type O blood?

Answer 1

R code:

count=0
count2=0
n=10 # No. of iterations

for(i in 1:n)
{
   x=runif(11) #Generating random number from uniform( 0 , 1)
   for(i in 1:11)
   {
       if(x[i]<.45) count=count+1 #counting the donners with o blood
   }
   if(count>=4)
    {
       count2=count2+1 #counting how meny times less than 12 donners needed
   }
   count=0
}
cat("The required probability is",(n-count2)/n)

Result:

The required probability is 0.2