a To use the random number generator function of a graphing calculator, push the MATH button, then scroll right to the PRB menu and choose the fifth option, randInt(.
B
b The average is the total sum of the values divided by the number of values.
A
a See solution.
B
bExample Answer: 6 games
Practice makes perfect
a In the World Series of baseball, the first team to win four games wins the championship. We want to design a simulation to estimate the expected value for the number of games that will be played in the World Series.
Let 1 represent Team 1 winning a game.
Let 2 represents Team 2 winning a game.
Let's use the random number generator in our graphing calculator. We will start by pushing the MATH button, then scrolling right to the PRB menu to choose the fifth option, randInt(.
After choosing this option, enter the minimum and maximum values of the set and the number of trials. In our case, we are only considering the values 1 and 2, so the minimum value is 1 and the maximum value is 2. Since the series may last up to 7 games, the number of trials is 7. Next, push ENTER.
We will repeat this simulation 25 times. Here is a table with the example results of our simulation.
Results
1 1 2 1 1 1 2
1 2 1 2 2 1 1
1 2 1 1 2 2 2
1 1 1 1 2 1 1
1 2 1 2 2 1 2
2 1 1 2 2 1 1
2 2 2 1 1 2 1
1 1 1 2 1 2 2
1 1 1 2 2 2 1
1 1 2 2 2 2 2
2 2 2 1 1 2 2
1 1 1 1 2 2 1
1 1 2 2 2 2 1
2 2 1 1 2 2 1
2 1 1 1 1 1 2
1 2 1 2 1 1 2
2 1 2 1 1 2 1
2 2 2 1 1 1 2
1 2 2 1 1 1 1
2 1 1 2 2 1 1
1 2 1 2 1 2 2
2 2 2 1 1 2 1
2 1 2 1 1 1 2
1 1 1 2 1 2 1
1 1 2 1 1 2 1
Remember, the first team to win 4 games wins the championship. In the first simulated championship, Team 1 won the first two games. Game 3 was won by Team 2, but Team 1 won another two games, which brought them to a total of 4 games won. All in all, Team 1 won the championships after a total of 5 games.
ccccccc 1 & 1 & 2 & 1 & 1 & 1 & 2 &(5 games)
& & & & 🥇& & & &
Let's record the number of games it took to win the World Series in each simulation. We will highlight the winning game of the championship.
Results
1 1 2 1 1 1 2 5 games
1 2 1 2 2 1 1 7 games
1 2 1 1 2 2 2 7 games
1 1 1 1 2 1 1 4 games
1 2 1 2 2 1 2 7 games
2 1 1 2 2 1 1 7 games
2 2 2 1 1 2 1 6 games
1 1 1 2 1 2 2 5 games
1 1 1 2 2 2 1 7 games
1 1 2 2 2 2 2 6 games
2 2 2 1 1 2 2 6 games
1 1 1 1 2 2 1 4 games
1 1 2 2 2 2 1 6 games
2 2 1 1 2 2 1 6 games
2 1 1 1 1 1 2 5 games
1 2 1 2 1 1 2 6 games
2 1 2 1 1 2 1 7 games
2 2 2 1 1 1 2 7 games
1 2 2 1 1 1 1 6 games
2 1 1 2 2 1 1 7 games
1 2 1 2 1 2 2 7 games
2 2 2 1 1 2 1 6 games
2 1 2 1 1 1 2 6 games
1 1 1 2 1 2 1 5 games
1 1 2 1 1 2 1 5 games
b Using the results from the table, we want to find the average number of games a World Series lasts.
Results
1 1 2 1 1 1 2 5 games
1 2 1 2 2 1 1 7 games
1 2 1 1 2 2 2 7 games
1 1 1 1 2 1 1 4 games
1 2 1 2 2 1 2 7 games
2 1 1 2 2 1 1 7 games
2 2 2 1 1 2 1 6 games
1 1 1 2 1 2 2 5 games
1 1 1 2 2 2 1 7 games
1 1 2 2 2 2 2 6 games
2 2 2 1 1 2 2 6 games
1 1 1 1 2 2 1 4 games
1 1 2 2 2 2 1 6 games
2 2 1 1 2 2 1 6 games
2 1 1 1 1 1 2 5 games
1 2 1 2 1 1 2 6 games
2 1 2 1 1 2 1 7 games
2 2 2 1 1 1 2 7 games
1 2 2 1 1 1 1 6 games
2 1 1 2 2 1 1 7 games
1 2 1 2 1 2 2 7 games
2 2 2 1 1 2 1 6 games
2 1 2 1 1 1 2 6 games
1 1 1 2 1 2 1 5 games
1 1 2 1 1 2 1 5 games
Let's add the numbers of games each World Series lasted and then divide the sum by the total number of simulations, 25.
5+7+ 7 + ... + 6+5+5/25 &= 150/25 [0.7em]
&= 6
According to our simulation, a Worlds Series, on average, lasts 6 games.
