Name _______________________________________________ Class__________________
SIMULATIONS
A simulation is a model of an experiment that would be difficult or inconvenient to actually
perform. In this lab, you will conduct simulations.
Activity 1
A cereal company is have a contest. To win a prize, you must collect six different cards that
spell YOU WIN. One of the six letters is put into each cereal box. The letters are divided
equally among the boxes.
How many boxes do you think you will have to buy to collect all six cards?
1) Since there are six different cards that are evenly distributed, you can use a number cube
to simulate collecting the letters. Each of the numbers from 1 to 6 will represent a letter. A
roll of the number cube will simulate buying one box of cereal, and number rolled will
represent the letter inside the box.
Roll the number cube and keep track of the numbers you roll. Continue to roll the number
cube until you have rolled every number at least once.
1
Y
2
O
3
U
4
W
5
I
6
N
2) Look at the results in the table above. What was the last number rolled? How do you
know?
3) How many rolls did it take to get all six numbers in your simulation?
4) How many boxes of cereal do you think you would have to buy to get all six letters?
5) If you bought the number of boxes that you indicated in #4, would you be sure to win?
Explain.
1
6) Repeat the simulation three more times. Record your results.
1
Y
2
O
3
U
4
W
5
I
6
N
7) List the number of “boxes” (rolls) it took in each of your four trials. Then get data from at
least four other people. You should end up with at least 15 pieces of data (or more). Find
the mean of all of the numbers you collected.
8) Now how many boxes of cereal do you think you would need to buy to get all six letters?
Is this number different than your answer in number 4? Explain.
Activity 2
Amy is a basketball player that usually makes ½ of the baskets that she attempts. Suppose
she attempts 20 shots in each game. If she plays ten games, in how many games do you
think she will make at least four baskets in a row?
There are two possible outcomes each time Amy shoots the ball—either she makes the shot
 or she doesn’t . Since Amy makes ½ of her shots, you can toss a coin to simulate her
shots. Let heads represent a basket and tails represent a miss.
1) Toss a coin 20 times for the first trial to simulate one game. Keep track of your results
below.
2) Repeat 9 times (you may share data in your group….maybe each student could flip for
two trials).
TRIAL
1
2
3
4
5
6
7
8
9
10
2
3) Why does tossing a coin 20 times represent only one trial?
4) Do any of your sequences contain four or more heads in a row? How many?
5) In how many games do you think Amy will make at least four baskets in a row?
6) Out of every 10 games, will Amy make at least four baskets in a row this number of times?
Explain.
7) You can use your simulation to find the experimental probability that Amy will make at
least four or more baskets in a row. Divide the number of trials in which the coin came up
heads at least four times in a row by the total number of trials. What is the experimental
probability that Amy will make at least four baskets in a row?
8) Suppose Amy made only 1/3 of her shots. Would you still be able to use a coin as a
simulation? Why or why not? If not, what could you use?
3