HOW WOULD YOU SOLVE THE FOLLOWING SCENARIOS? If we know the blood types of a man and a woman, what can we say about the blood types of their future children? An opinion poll asks a sample of 1500 adults what they consider the most serious problem facing our schools. How often will the percent of those who answer “drugs” come with in two percentage points of the truth about the entire population? Is it possible to determine if a lottery is rigged?

3 WAYS TO SOLVE QUESTIONS INVOLVING CHANCE Estimate Frequency by observing random phenomenon many times Develop a probability model and calculate a theoretical answer (6.2) Create a model that simulates the random phenomenon (6.1)

PROBABILITY Number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions

CHAP 6.1 SIMULATIONS

SIMULATION The imitation of chance behavior, based on a model that accurately reflects the phenomenon under consideration

4 STEPS TO SIMULATION *SIMPLIFIED FROM 5 STEPS IN THE BOOK 1.STATE: What is the question of interest? 2.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 DO

INDEPENDENT TRIALS One outcome has no influence over the probability of another outcome Which are Independent situations? Flipping coins Drawing a card from a deck with replacement Drawing a card from a deck without replacement

6.1 Assignment: pg. 15, 16, 19, 20