Of ProbabilityEXPLORING CONCEPTS

1.Chance has no memory. For repeated trials of a simple experiment, the outcomes of prior trials have no

impact on the next trial.2. The probability that a future event will occur can be characterized along

a continuum from impossible to certain.

BIG IDEAS

3. The probability of an event is a number between 0 and 1 that is a

measure of the chance that a given event will occur.

4. The relative frequency of outcomes can be used as an estimate of the probability of an event. The larger the number of trials the better the

estimate will be.

BIG IDEAS

5. For some events, the exact probability can be determined by an analysis of the

event itself.

6. Simulation is a technique used for answering real-world questions of making decisions in complex situations in which an

element of chance is involved.

BIG IDEAS

ConnectionsCONTENT

Fractions and Percents (15 and 17) Students can see fractional parts of spinners or sets of counters in a bag

and use these fractions to determine probabilities. Percents provide useful common denominators for

comparing ratios. Ratio and Proportion (18) Comparing probabilities means relating part-to-whole ratios. to understand these

comparisons requires proportional reasoning. Data Analysis (21) The purpose of probability is to answer the statics-related question. When performing a probability experiment, the results are data- a sample of the theoretically infinite experiments that could be done.

PROBABILITY IS GROUNDED IN CONCEPTS OF RATIONAL NUMBER

AND DATA ANALYSIS.

PROBABILITY Is about how likely an event is.

Impossible? or Possible?It will rain tomorrow.

Drop a rock in water and it will sink.A sunflower seed planted today will bloom tomorrow.

The sun will rise tomorrow morning.A tornado will hit our town.

If you ask someone who the first president was, they will know.

You will have two birthdays this year.

You will be in bed by 9:00 p.m.

IS IT LIKELY?

Before: Students make predictions of what they think will likely.

During: Students experiments to explore how likely the event is.

After: Students compile and analyze the experimental results to determine more accurately how likely the event

is.

THE PROCESS OF EXPLORING HOW LIKELY AN

EVENT IS.

THEORETICAL PROBABILITYAnd Experiments

Of an event is a measure of the chance of that event occurring.

PROBABILITY

1. Involves any specific event whose

probability of occurrence is

known. When the probability of an event in known,

probability can be established

theoretically by examining all the

possibilities.

2. Involves any event whose probability of

occurrence isn't observable but can

be established through empirical data or evidence

from past experiments or data

collection.

PROBABILITY HAS TWO DISTINCT TYPES

Rock Paper Scissors

THEORETICAL PROBABILITY

EXPERIMENTS

Toss cup in air 20 times and land on floor, record how it lands (upside down, right side up, or on its side), discuss the results.

DROP IT!

Model real-world problems that are actually solved by conducting experiments.

Provide a connection to counting strategies to increase confidence that the probability is accurate.

Provide an experiential background for examining the theoretical model

Help students see how the ratio of a particular outcome to the total number of trials begins to

converge to a fixed number. Help students learn more than students who do not

engage in doing experiments.

WHY USE EXPERIMENTS?

SAMPLE SPACES AND PROBABILITY OF TWO

EVENTSSample Space: Experiment or chance situations is

the set of all possible outcomes for that experiments.

EVENTA subset of the sample space.

One Event

Examples:Rolling a single die

Drawing one colored tile from a bag

Occurrence of rain tomorrow

Two Event

Examples:Rolling two dice

Drawing two tiles from a bag

Combination of both the occurrence of rain and

forgetting your umbrella.

EVENT EXPERIMENTS

Independent

The occurrences of nonoccurrence of one event has no

effect on the other.

Dependent

The second event depends on the

result of the first.

TWO EVENT EXPERIMENTS

SIMULATIONSTechnique used for answering real-world questions or making decisions

in complex situations where an element of chance is involved.

1) Identify key components and assumptions of the problem.

2) Select a random device for the key components.

3) Define a Trial. Trial: consists of simulation a series of key components until the situation

has been completely modeled on time.4) Conduct a large number of trials and record

the information.5) Us the data to draw conclusions.

STEPS FOR SIMULATION

http://www-k6.thinkcentral.com/content/hsp/math/hspmath/ca/

common/itools_int_9780153616334_/

probability.html

GAME

http://www.bing.com/videos/search?q=2nd+grade+probability&view=detail&mid=44F50045A79DBE52794644

F50045A79DBE527946&first=0

3D ANIMATED MATH PROBABILITY SPINNER

VIDEO

http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell19.swf

PROBABILITY