Of Probability

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 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

Connections

 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 PROBABILITY And Experiments

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

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

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 EVENTS Sample Space: Experiment or chance situations is the set of all possible outcomes for that experiments.

EVENT A 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

SIMULATIONS Technique 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

k6.thinkcentral.com/content/hsp/math/hs pmath/ca/common/itools_int_ _/probability.html GAME

de+probability&view=detail&mid=44F50045A79 DBE F50045A79DBE527946&first=0 3D ANIMATED MATH PROBABILITY SPINNER VIDEO

=lessons&lesson=m6lessonshell19.swf PROBABILITY