Upload
jean-ferguson
View
217
Download
0
Embed Size (px)
DESCRIPTION
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 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
Citation preview
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