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