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Designing Simulations with Technology
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SECTION 7-7-8Designing Simulations with Technology
WARM-UP
Go to the wiki and click on the “Stick or Switch” link under Sections 7-7 and 7-8. Use this virtual manipulative to
complete the in-class activity on page 464.
What strategy should the contestant use? Stick? Or Switch?
Simulation:
Simulation: An experiment that models a situation while considering all possible outcomes and situations
Simulation: An experiment that models a situation while considering all possible outcomes and situations
Monte Carlo Method:
Simulation: An experiment that models a situation while considering all possible outcomes and situations
Monte Carlo Method: A method that utilizes relative frequencies from repeated trials
Simulation: An experiment that models a situation while considering all possible outcomes and situations
Monte Carlo Method: A method that utilizes relative frequencies from repeated trials1. Determine a simulation to use
Simulation: An experiment that models a situation while considering all possible outcomes and situations
Monte Carlo Method: A method that utilizes relative frequencies from repeated trials1. Determine a simulation to use2. Determine what a single trial is and what data will be collected
Simulation: An experiment that models a situation while considering all possible outcomes and situations
Monte Carlo Method: A method that utilizes relative frequencies from repeated trials1. Determine a simulation to use2. Determine what a single trial is and what data will be collected3. Choose a number of times to run the trial and how to obtain an answer
WAYS TO RUN SIMULATIONS
WAYS TO RUN SIMULATIONS
Dice
WAYS TO RUN SIMULATIONS
Dice
Cards
WAYS TO RUN SIMULATIONS
Dice
Cards
Random numbers
WAYS TO RUN SIMULATIONS
Dice
Cards
Random numbers
Flip a coin
WAYS TO RUN SIMULATIONS
Dice
Cards
Random numbers
Flip a coin
Spinners
WAYS TO RUN SIMULATIONS
Dice
Cards
Random numbers
Flip a coin
Spinners
What else?
EXAMPLE 1
Four darts are thrown randomly at a coordinate plane and the quadrants in which they land are recorded. If the dart
lands on an axis, it is thrown again. It is desired to simulate the probability that all four darts land in at most two of the quadrants. That is, if 1 dart lands in Q1 and 3 darts land in
Q3, then there is a success. Design a simulation with 50 trials to estimate this probability.
TABLE OF RANDOM NUMBERS
TABLE OF RANDOM NUMBERS
Refer to Appendix C on page 874.
TABLE OF RANDOM NUMBERS
Refer to Appendix C on page 874.
When each number has the same probability of occurring
TABLE OF RANDOM NUMBERS
Refer to Appendix C on page 874.
When each number has the same probability of occurringWhen each pair has the same probability of occurring
TABLE OF RANDOM NUMBERS
Refer to Appendix C on page 874.
When each number has the same probability of occurringWhen each pair has the same probability of occurring
When each triple has the same probability of occurring
TABLE OF RANDOM NUMBERS
Refer to Appendix C on page 874.
When each number has the same probability of occurringWhen each pair has the same probability of occurring
When each triple has the same probability of occurringEtc.
TABLE OF RANDOM NUMBERS
Refer to Appendix C on page 874.
When each number has the same probability of occurringWhen each pair has the same probability of occurring
When each triple has the same probability of occurringEtc.
To use the table, work randomly!
PROB SIM ON THE TI
PROB SIM ON THE TIAllows us to run probability simulations using technology
PROB SIM ON THE TIAllows us to run probability simulations using technology
Apps --> Prob Sim
PROB SIM ON THE TIAllows us to run probability simulations using technology
Apps --> Prob Sim
PROB SIM ON THE TIAllows us to run probability simulations using technology
Apps --> Prob Sim
RANDOM NUMBERS ON THE TI
RANDOM NUMBERS ON THE TIMath --> PRB
RANDOM NUMBERS ON THE TIMath --> PRB
RANDOM NUMBERS ON THE TIMath --> PRB
Round it off:
RANDOM NUMBERS ON THE TIMath --> PRB
Round it off:
RANDOM NUMBERS ON THE TIMath --> PRB
Round it off: Random Integers
RANDOM NUMBERS ON THE TIMath --> PRB
Round it off: Random Integers
EXAMPLE 3
A particular state lottery has a game in which a winner receives $10 for $1 entry, but only 3 in 50 entries win. Explain
how to use technology to simulate the results of 100 bets.
EXAMPLE 4
Matt Mitarnowski has a batting average of .250. In his next 10 at bats, what is the probability that he gets exactly 3 hits?
Run a simulation to determine this situation.
EXAMPLE 5
What could be used as a simulation when the following ratios are given?
a. 1:2 b. 1:4 c. 1:6
HOMEWORK
HOMEWORK
p. 468 #1, 4-10; p. 476 #1-3, 10-17