Conclusion of Probability

So what have we learned about probability?? Let's review...

 Probability is about chance... what chances do you have of winning, losing, drawing a card?
Odds is about comparing winning to losing, how many times can you win an event or lose an event?

Example:

 What is the probability of drawing a King from a deck of cards?
                                                       4/52= 1/13
 What are the odds of drawing a King from a deck of cards?
                                                      4/48= 1/12 

Theoretical Probability can be found mathematically without and experiement and the results will not vary

Example:  
Tossing a coin will always be 1/2 or 50% of getting heads/tails

Experimental Probability is the result of an observation, the numbers are unique to each experiment  

Example:
Drawing a marble from a bag, the numbers will vary on how many marbles you have total and how many trials conducted.

I believe that probability is an important part of the ccurriculum for what students learn in elementary school.  It is important for future teachers to fully understand it.  I enjoyed sharing what I learned in the past posts and will always have them to look back on!!

http://mathandreadinghelp.org/teaching_probability_to_kids.html 
 This link provides an article for math helpful tips for teachers and parents on teaching children probability! 

 

Multistage Experiments with Tree Diagrams

Multistage Experiments Include.....

One-Stage Experiment-  experiments that are over after one step
 Two-Stage Experiment-  experiments that require many trials to complete
 Geometric Probabilities-  a probability model that uses geometric shapes as an area model

When we document our results for multistage experiments it helps to draw...

A tree diagram!!
 Let's look at an example:
If we have three colored marbles in a bag (two red and one blue) and are going to draw two out and then replace them then this is what the tree diagram would look like:

  


  The outcomes you get from each draw is listed in the diagram
   You then would proceed to multiply together the outcomes and find the probability of each color combo being drawn.   



If we conducted the same experiment but do not replace the marbles into the bag, the fractions would be different.  Each time you take a marble out, the total number (in the denominator) goes down.  

http://www.regentsprep.org/Regents/math/ALGEBRA/APR4/PracTre.htm 
This link has tree diagram questions for practice, not just with probability but with word problems as well!!
    

 

What are the Odds?

Now we begin to learn something new.... Odds

This is not to be confused with probability, odds is similar but a different concept

Definition:  the likelihood of an event
Odds= Number of successes 
              Number of failures 

Here is an example:

*What are the odds of drawing a queen in a deck of cards?
 There are 4 queens in a deck of cards; this is the numerator
There are 52 cards in one deck so subtract 4 from 52 to get the denominator 
the answer is   4/52 reduced to 1/13
so the odds of getting a queen is 1:13

                                                        
Have you seen the difference yet of odds and probability? Let me explain.
Odds is finding the possible wins to the possible loses in an event.
Probability is looking at the chances of an outcome out of the total event. 

We can look at odds from two different standpoints: 

   **Odds in favor of an event- Number of ways that an event could occur
                                                       Number of ways that the event could not occur

    **Odds against an event-  Number of ways that an event could not occur
                                                    Number of ways that the event could occur
So basically, when writing out the two different ways you just switch the numerator and denominator for the answer

Odds in favor of queen in a deck of cards- 1:13
Odds against getting a queen in a deck of cards-  13:1

Here is a video that shows random odds in our world and how rare events actually are... very interesting WATCH IT! 
 

 

Confusion with Probability

 There were some things that stumped me with probability.....

Mutually Exclusive Events-  If an event A occurs then event B cannot occur; if they have no elements in common

This was confusing to grasp but I understood the concept by looking up another definition online.  Basically Mutually Exclusive means that two events are unable to be true at the same time

 I liked this picture because it shows the Venn diagram of events A and B and how they can not intersect with on another.  The probability of events A and B in union is adding event A and event B. 

Next word problems......

Word problems have always been a problem for me all throughout learning math!  I am a very visual person and need pictures and diagrams to understand.  Here is an example of a word problem that stumped me:

* There is a pond of frogs and 50 frogs are caught, marked, and thrown back into the pond.  Then there were 80 frogs caught and 20 of them were marked. What is the population of the pond?

To solve this problem we make a proportion:
20/80=50/x    
 This proportion is comparing frogs marked to the starting number of frogs in the pond and x is the total pond population.
20x=4000
x=200 total frogs in pond

So once I visually made a picture in my head, this proportion made sense for solving the problem.

These two concepts were difficult for me to understand but with manipulatives I was able to grasp the idea!

                                                        
 
http://www.mathsisfun.com/data/probability-events-mutually-exclusive.html
This link helped me with the definition of mutually exclusive events and gave me examples as well!

Introduction to Probability

Probability... What's it all about?


Have you ever flipped a coin, rolled a dice, or spun a spinner?  Ever thought of what the chance of rain or sunshine is for the day?  These are all examples of probability. 

By definition:  Probability is the likelihood that a particular event will occur
* number of outcomes is compared to the total number of outcomes.

How are probabilities are determined: We start with an experiment; an activity whose results can be observed and recorded.  Then we look at all the possible outcomes that could come from the experiment.  When rolling a die, what are the chances of rolling a 4?  This is an example of an outcome or a possible result of an experiment.  The sample space is a set of all possible outcomes for an experiment.  So when rolling a die, the sample space is S= 1,2,3,4,5,6. 

Types of Probability:
Experimental (empirical) -  result of an observation where the numbers are unique to each experiment Ex. a spinner with different number increments
Theoretical - can be found mathematically without an experiment and the results will not vary 
Ex. tossing a fair coin, results are heads/tails

http://www.free-training-tutorial.com/probability-games.html
Above is a link for free online educational games.  I played the probability game and it was basic practice of introductory probability.

A Little Bit About Elissa

Elissa Spina
21 years old
Future Special Education Teacher 

Hello Everybody welcome to my blog!  Blogging is all new to me but I am very excited to get involved with it and play around.  I consider this my online math journal and will add things I learn throughout my college years.

Now a little bit about me....

My name is Elissa and I am currently in my last semester at Mesa Community College.  Have been attending MCC for the past three years and I am excited to finish.  I will be attending Arizona State University Fall of 2013 to complete my bachelors degree in Special Education and Elementary Education.  I am very excited for this next chapter of my life and I can finally begin to see a light at the end of the tunnel!  What an amazing feeling to have two years left of school and then I will be a certified teacher!  I am very excited for the future and can't wait for what's to come.

Why I want to be a teacher.....

I have known I have wanted to be a teacher since seventh grade.  This was when I started volunteering at my junior high with the special needs classroom and I really developed a love for these students.  I always knew I was different from other kids when I was younger because I would look at special needs students differently.  I can remember all the way back to first grade when I made friends with a specials needs girl on the playground. Although she was in a wheelchair, I didn't see her any differently than any other person and considered her a good friend.  So from the time I was younger, special needs people fascinated me and I wanted to learn from them.  All throughout junior high I volunteered in the PALS program and Mrs. Shown was the teacher in this classroom.  She was the one who really inspired me to love these kids, have patience with them, and made me want to be a teacher.  I learned a lot from this program and about the different behaviors of mentally challenged students.  I am currently working at Keller elementary school as an Instructional Assistant for the Occupational Therapist.  This job has required me to work with all levels of special needs students of all ages.  I enjoy being around other teachers, learning from them, and seeing what makes them successful.  So here I am today and I cannot wait to have my own classroom!!