7th Grade
24 c. Design and use a simulation to generate frequencies for compound events. [7-SP8c]
Example: Use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A
blood, what is the probability that it will take at least 4 donors to find one with type A blood?
To simulate the question asked above, we could take the ten digits ( 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 ) and let 40% of them
represent those donors with Type A blood. So let’s say that we let the digits 0, 1, 2, 3 represent Type A donors and the
remainder of the digits (4, 5, 6, 7, 8, 9) represent the 60% of the donors not having Type A blood.
We want to find the probability that it will take at least 4 donors to find one with Type A blood. Thus, we want to find the
probability that we do not get a Type A blood donor in the first 3 random picks. In other words, we want to find the
probability that we do not generate a 0, 1, 2, or 3 within the first three picks.
The TI-73 or TI-83/84 graphing calculators can be excellent tools to use in the simulation of the example noted in this
standard. Prior to using the random features of the calculator, it is important to seed each calculator with its own “random
number seed” so that all calculator results are not the same---based upon the fact that they all come from the factory with
the same seed number. To do this, type any 5 or 6 digit number into the calculator, push the STO button and then the
MATH key over to PRB, then rand, and ENTER twice. Make sure each calculator has a different seed number. Now to
generate random digits, you push the MATH button, scroll over to PRB at the top and then go down and highlight
randInt( . Since we want to generate 3 random digits and then determine whether or not any have Type A blood, type
the following after the command randInt(0, 9, 3) meaning we want the calculator to randomly generate digits from 0
to 9 and we want it to generate 3 of these. Press ENTER to see the 3 digits generated. Look at the three digits and
record whether or not TYPE A donor was found in the first three randomly generated numbers. In other words, does the
set of three numbers include at least one of 0, 1, 2, or 3. If so, we found a Type A donor in less than 4 trials. Press
ENTER again and you will see another set of numbers. Keep pressing ENTER and record the results for at least 50 times.
(Or you can have students do this five times each and then combine results for a total of 150-200 trials.)
Numbers Type A
Generated (0,1,2,3)
Within
first
three
trials
9,1,3
8,5,3
8,6,2
0,7,4
2,6,8
8,6,5
7,7,3
Not
Type
A
Within
first
three
trials
X
X
X
X
X
X
X
In the example above, the probability of it taking at least 4 donors to find one with type A blood is the
same as the probability that it did not happen within the first three trials. Thus, the experimental
probability is 1/7 or 0.14. The actual probability is 0.216. This experimental answer should get closer to
the theoretical answer of 0.216 as the number of trials increases.