DESIGNING SIMULATIONS
Section 7.7
Monty Hall Problem
Break up into teams of 2
and complete the activity
on page 464. Fill in the
chart for number 5, and
answer questions 6 and
7.

Definitions


Simulation: a way to test the
results of an experiment without
actually conducting the
experiment.
Trial: each repetition of the
experiment
Monte Carlo Simulations
1. determine how it will be simulated
 2. Define what constitutes a single trial and
what data will be recorded.
 3. Specify the number of trials that will be
run and how the estimated answer will be
obtained.

**very helpful – p. 874 (random numbers)
BEGIN AT ANY NUMBER(not beginning)!!!
Example 1

Four darts are thrown randomly at a coordinate
plane and the quadrants are recorded. It is
desired to simulate the probability that all 4
darts land in at most 2 quadrants. Design a
simulation with 50 trials to estimate this
probability.
Sample: roll two dice, 1 – 4 stand for quadrants.
Re-roll if it lands on 5 or 6. Roll die 4 times –
record answer. Repeat 50 times.
Example 2

Explain how to use a table of random
numbers to simulate the trials in Example 1.
Take the numbers in pairs. If the number is
between
0 – 24  quad 1 Look at 8 numbers. Record results.
25 – 49  quad 2 Repeat 50 times!
50 – 74  quad 3
75 – 99  quad 4
Example 3

Run the simulation mentioned in example 2.
I began my random number at row 23, column 10.
1, 4, 1, 3
1, 3, 1, 1
4, 4, 1, 4 …
18 / 50 = .36
Theoretical probability:
1/16 + ¼ + 1/16 = 3/8
Homework
Page 469
3, 4, 6 – 8
(skip 8 b)