5.1 RANDOMNESS, PROBABILITY, AND SIMULATION
1. Pretend that you are flipping a fair coin. Without
actually flipping a coin, imagine the first toss.
Write down the result you see in your mind,
heads (H) or tails (T).
2. Imagine a second coin flip. Write down the result.
3. Keep doing this until you have recorded the
results of 50 imaginary flips. Write your results in
groups of 5 to make them easier to read, like this:
HTHTH TTHHT, etc..
4. Set this aside…you will need it later!
1 IN 6 WINS GAME
• Do the activity on page 288 with a partner.
• Instead of making a class dot plot, make a dot for just your
results
• Follow the activity until you have 20 points on your dot
plot
• This means you will roll the die a total of 140 times!
• Don’t forget your labels and such
3 WAYS TO SOLVE QUESTIONS INVOLVING
CHANCE
• Estimate Frequency by observing random
phenomenon many times
• Develop a probability model and calculate a
theoretical answer (5.2)
• Create a model that simulates the random
phenomenon (5.1)
CHAP 5.1 SIMULATIONS
PROBABILITY
• Number between 0 and 1 that describes the proportion of
times the outcome would occur in a very long series of
repetitions
• Law of Large Numbers:
• more and more repetitions of any chance process,
• the proportion of times that a specific event occurs will
approach a single value
• http://digitalfirst.bfwpub.com/stats_applet/stats_applet_10_
prob.html
• Activity page 293
SIMULATION
• The imitation of chance behavior, based on a
model that accurately reflects the phenomenon
under consideration
4 STEPS TO SIMULATION
1.
2.
STATE: What is the question of interest?
PLAN: Describe how to use a chance device to imitate one
repetition of the process.
Explain clearly how to identify the outcomes of the chance
process and what variable to measure.
3. DO: Perform many repetitions of the simulation.
4. CONCLUDE: Use the results of your simulation to answer the question
of interest.
AP Exam Tip: You may receive full credit for solving a problem by simulation
even if the problem does not call for it.
EXAMPLE 1
STEP 1 STATE
STEP 2 PLAN
STEP 3 DO
STEP 4 CONCLUDE
HOMEWORK: 5.1 (PG. 300) #3, 7, 9, 15-17 ODD, 23, 25,
31-36 ALL