

Course 1, Unit 8  Patterns in Chance
Overview
The Patterns in Chance unit introduces students to sample spaces,
probability distributions, the Addition Rule, simulation, and geometric
probability. Important probabilistic concepts explored include mutually
exclusive events and the Law of Large Numbers.
In Lesson 1, students learn to use sample spaces and probability
distributions to calculate probabilities. In Lesson 2, students
learn how to estimate probabilities using simulation and random number
generators and how to calculate probabilities using geometric (area)
models.
Simulation is the modeling of a probabilistic situation using random
devices such as coins, spinners, and random digits. Simulation is useful
throughout instruction on probability. Setting up a simulation helps
students clarify their assumptions about such things as whether trials
are independent. Simulation helps develop students' intuition about probabilistic
events. And, perhaps most importantly, students who have been introduced
to simulation have a feeling of control over probability. They know that
they can estimate the answer to any probability problem that arises.
Key Ideas from Course 1, Unit 8

Probability distribution: a description of all possible numerical
outcomes of a random situation, along with the probability that each
occurs. The description may be in table, formula, or graphical form. (See
p. 534.)

Mutuallyexclusive events: Two events are said to be mutually
exclusive (or disjoint) if it is impossible for both
of them to occur on the same outcome. (See p. 537539 for
the development of this idea.)

Addition Rule: The rule for computing the probability that
event A or event B occur is developed on p. 540.

Simulation model: a way of modeling a real situation that
involves randomly occurring events. For example, suppose that 45%
of a population has type O blood. Here's how to use simulation to
estimate the probability that 4 random people entering a blood donor
bank have blood type O. Model the selection of one person chosen
at random from the population by assigning the numbers 145 to represent
people with type O blood and 46100 to represent other people. Choosing
4 numbers at random from 1 to 100 and counting how many are 145
would simulate 4 random people entering a blood donor clinic and
being identified by blood type. Simulations can be run using the CPMPTools public
domain suite of software tools. (See p. 553.)

Law of Large Numbers: The Law of Large Numbers says that
the more runs there are in a simulation, the better your estimate
of the probability tends to be. (See p. 555.)

Geometric probability: Area models can be used to model chance
situations where the numbers are selected at random from a continuous
interval. (For an example, see p. 568 Problem 1.)
