The Iowa State basketball team needs to win 3 straight games to win the Big 12 t

Question

The Iowa State basketball team needs to win 3 straight games to win the Big 12 tournament. The points that Iowa State will score follows a Triangular distribution with a minimum = 51, most likely = 66, and maximum = 75.
The points that Iowa State's first opponent will score follows a Triangular distribution with a minimum = 60, most likely = 74, and maximum = 81.
The points that Iowa State's second opponent will score follows a Triangular distribution with a minimum = 53, most likely = 63, and maximum = 66.
The points that Iowa State's third opponent will score follows a Triangular distribution with a minimum = 59, most likely = 60, and maximum = 71.
Assume that the Triangular distribution for Iowa State remains the same for all 3 games. Simulate the number of points that Iowa State will score in each game and the number of points that each of its opponents will score using the above distributions with 100,000 trials. Define three output cells as the difference in points between Iowa State and each opponent. Use ""countif"" to calculate the probability that Iowa State beats each opponent (i.e., the probability that ISU points - opponent points > 0). What is the probability that Iowa State wins all three games? Express your answer as a decimal between 0 and 1."

The Iowa State basketball team needs to win 3 straight games to win the Big 12 tournament. The points that Iowa State will score follows a Triangular distribution with a minimum = 51, most likely = 66, and maximum = 75.
The points that Iowa State's first opponent will score follows a Triangular distribution with a minimum = 60, most likely = 74, and maximum = 81.
The points that Iowa State's second opponent will score follows a Triangular distribution with a minimum = 53, most likely = 63, and maximum = 66.
The points that Iowa State's third opponent will score follows a Triangular distribution with a minimum = 59, most likely = 60, and maximum = 71.
Assume that the Triangular distribution for Iowa State remains the same for all 3 games. Simulate the number of points that Iowa State will score in each game and the number of points that each of its opponents will score using the above distributions with 100,000 trials. Define three output cells as the difference in points between Iowa State and each opponent. Use ""countif"" to calculate the probability that Iowa State beats each opponent (i.e., the probability that ISU points - opponent points > 0). What is the probability that Iowa State wins all three games? Express your answer as a decimal between 0 and 1."

0.052

Explanation / Answer

I have done this using R . The codes to calculate the three cells of output difference and the probability of lowa state wins all three games are given below:

library(triangle)
count=NULL
l1=rltriangle(10000,51,75,66)
op11=rltriangle(100000,60,81,74)
d1=l1-op11
l2=rltriangle(100000,51,75,66)
op22=rltriangle(100000,53,66,63)
d2=l2-op22
l3=rltriangle(100000,51,75,66)
op33=rltriangle(100000,59,71,60)
d3=l3-op33
for(i in 1:100000)
if(d1[i]>0 && d2[i]>0 && d3[i]>0)
{ count=count+1}
p1=count/100000

where d1,d2,d3 are the difference between the lowa state and opponent in game1,game2,game3 respectively where p1 is the probability of lowa state to win all three matches.

Alternative way to calculate the probability is given by following R code:

f= function(a=51, b=75,c=66)
{
l1=rltriangle(1,a,b,c)
op11=rltriangle(1,60,81,74)
l2=rltriangle(1,a,b,c)
op22=rltriangle(1,53,66,63)
l3=rltriangle(1,a,b,c)
op33=rltriangle(1,59,71,60)
count=NULL
if(l1>op11 && l2>op22 && l3>op33)
{count=1}else
{count=0}
count
}
s=100000
d=t(replicate(s, f()))
p2=(length(which(d==1)))/(length(d))

Here I have defined a function where we count no of winning all three matches by lowa state and then simulated 10000 times to calculate p

The calculated value of probability is 0.0499

In excel you can use countif() function where you add three columns d1,d2,d3 rowwise and make another column and see countif(Range,">0") then dividing by 10000 we will get the required probability. At first you have to extract the data of d1,d2,d3 from R to excel and then compute the desired probability.

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