Unit 5: Probability—What are the Chances? Intro Activity Using simulation

5.1 Randomness, Probability and Simulation

Big Idea: Big Idea: Big Idea: Chance determines outcome Big Idea: Chance behavior is unpredictable in the short term Big Idea: Chance behavior has a regular and predictable pattern in the long term

Let’s explore tossing a coin But we will use our calculator as a stand-in for the coin In other words, we will simulate tossing a coin by using the randInt function

That single value is called the probability of the outcome. Law of Large Numbers: As the number of repetitions of a chance process approaches infinity, the proportion of times that a single outcome occurs approaches a single value. That single value is called the probability of the outcome.

Probability of an event E: 1. 0 ⦤P(E)⦤ 1

Myths of Randomness: 1. Short-run regularity 2. Law of Averages

Duck Shoot   There are 12 siblings at a shooting gallery at the state fair. Each is a perfect shot. Twelve cardboard ducks appear simultaneously, and each sibling picks one of the twelve ducks at random and hits her/his target. We will assume that each player is allowed only one shot.

It is unlikely that each of the twelve shooters will pick a unique duck to shoot. Therefore it is likely that one or more of the twelve ducks will “survive.” But how many?

It would be tedious to write out a list of all possible outcomes of this experiment. Agree or disagree? (If you disagree, then I expect you to write them all out!) On average, how many ducks would you guess would survive?

Let’s Simulate! Clearly explain the chance process that imitates the actual activity Clearly explain what variable is being measured Explain one repetition Perform many, many repetitions