CHS Statistics
3.6: Probabilities Through Simulations
Objective: To simulate probabilities
using random number tables and
random number generators
Probabilities Through Simulations
• Sometimes we are not sure our theoretical probability is
correct.
• To check we can conduct actual trials or collect real data
to find probability value or verify that our theoretical
results are correct.
• Remember that the Law of Large Numbers tells us that
the more trials were conduct, the closer our
experimental probability will get to our theoretical
probability.
• We can also simulate the circumstances to learn how the
results would occur in reality.
Simulation
• A simulation of a procedure is a process that
behaves the same way as trials of an experiment,
so that similar results are produced.
• To perform a simulation, you must assume that the
“trials” are independent from one another.
Simulation Example:
• When testing techniques of gender selection, medical
researchers need to know probability values of different
outcomes, such as the probability of getting at least 60 girls
among 100 children. Assuming that male and female births
are equally likely, describe a simulation that results in the
genders of 100 newborn babies.
• We could flip a coin 100 times and let Heads represent
girls and tails represent boys, but who wants to do this?
Random Number Generators
• Instead of flipping coins, we can use random number generators:
• Random Digits Tables: These digit have been randomly
generated. Recall its use from Chapter 1.
• Graphing Calculator: Recall that we can use randInt in the
graphing calculator. Go to Math  PRB  randInt(
• Online Random Number Generators: There are many
random number generators available online.
• Random Number Generator Software: There are many
software packages with random number generators. MiniTab
is one of them. We will use this software later in the course.
Baby Example:
• Let’s go back to the baby example: When testing techniques of gender
selection, medical researchers need to know probability values of different
outcomes, such as the probability of getting at least 60 girls among 100
children. Assuming that male and female births are equally likely, describe
a simulation that results in the genders of 100 newborn babies.
• Let’s practice using the random number table.
• Since the chances of having a boy and a girl are equally
likely, we want to consider the assignment of single digits 0-9:
• How can we simulate this scenario in the calculator?
Dice Simulation:
• Describe a procedure for simulating rolling two dice and finding the
sums.
Free Throws:
• Suppose a basketball player has an 80% free throw success rate. How
can we use random numbers to simulate whether or not she makes a
foul shot? How many shots might she be able to make in a row
without missing?
Free Throws (Again):
• How would our simulation procedure change if her success rate were
only 72%?
Assignment
AP Statistics- Chapter 11 Quiz