Probability and Odds in the Real World

I hope that I have shed some light on the world of probability and odds and that you can now go forth in tackling these problems with confidence. I think that it is important to note that probability is all around us. It is not simply something that you will learn and use within the confines of a classroom. Here are some examples of practical, real-life uses of probability and odds:

• When planning a picnic! What?! you probably think I'm crazy, but it's true. Before packing your basket, you had better check the weather. If there is a 70% chance of rain, do you think it would be wise to head out for a picnic? How about a 20% chance? Are you getting it now? Probability makes a huge difference!

• When making medical decisions. This is a bit more serious but oh-so-true. If a doctor tells you that the odds of a procedure being successful are 100:1, it may be beneficial to consider the procedure. However, if the odds of a procedure being successful are 1:100, you may want to explore other options. Either way, you had better know the difference between these 2 different odds!

• When gambling! While I am not a gambler and do not condone the practice, knowing odds and probability can help you make an informed decision about whether or not to gamble. The odds of winning the lottery, for example, are so miniscule that I choose not to participate. However, the odds are different everyday depending on the number of ticket sold. Some may choose to buy a ticket when the jackpot is low because there is a higher probability of winning (even though there is a lower payout). Others may choose to play the lottery when the jackpot is a very high number, despite the fact that the probability of winning is not as good.

Probability is all around us! Here is a link to even more real-world applications:

http://www.ehow.com/list_7719506_real-life-probability-examples.html 

Please comment on my blog or contact me if you have any questions or if you would like further explanation about probability and/or odds. I am always happy to help!

Thank you!

~ Tammy

The Odds of Confusing Probability with Odds

Or should I say the probability of confusing odds with probability?

Either way, it is very important to note that odds and probability have some major differences.

Lets first review the equations for finding probability (P) and odds (O):

(P) =   # of desirable outcomes                (O) =   # of desirable outcomes  

           # of possible outcomes                         # of undesirable outcomes

I encourage you to look at these equations analytically for a moment and try to imagine how you might change probability to odds and vise-versa using your prior algebraic knowledge. If you are able to figure it out on your own, GREAT! I always retain information better if I am able to solve the problem on my own. I guarantee that you will remember your own thought processes better than you remember my instructions, so please take a moment and just THINK! :)

If you were unable to figure it out on your own, please read on. Even if you think you have the solution, it may be best to also read on in order to gain a better understanding.

Here's an example (you know I love EXAMPLES!):

If you enter into a raffle, would you rather the probability of winning be 49/100 or the odds of winning be 49 : 100?

In order to figure this out, you need to first know how to convert probability to odds and/or odds to probability.

Easy peasy, lemon squeezy!

Converting probability to odds:

- subtract the numerator (# on top) from the denominator (# on bottom) to determine the # of unfavorable outcomes:

P =   49    

       100

100 (# of poss. outcomes) - 49 (# of favorable outcomes) = 51 (# of unfavorable outcomes)

Since you now know the # of unfavorable options, you can figure out the odds:

49 : 51

Converting odds to probability:

- add both sides of the ratio to determine the denominator.

O = 49 : 100

49 + 100 = 149 (new denominator)

So, P = # of favorable outcomes

                          149

Based on the information that you already know, the first # in a ratio shows that # of favorable outcomes.

So..............

P =   49  

       149

Now that you have made your conversions, let's return to our original question:

If you enter into a raffle, would you rather the probability of winning be 49/100 or the odds of winning be 49 : 100?

I prefer to use probability, so here is what we are comparing:

P =    49            OR            P =    49    (O = 49:100)

        100                                     149

Which would to prefer? If you're still not sure, divide for a percentage:

49/100 = 49%         49/100 = 33% 

I'm going with the first one! :)

I hope that this post has helped to illustrate the difference between odds and probability. For further exlantation, visit the following web address: http://www.math-magic.com/probability/prob_to_odds.htm.

For another fun and interesting explanation and to test your knowledge, check out the video below!  

 Thank you for stopping by! Have a wonderful evening!

~ Tammy

May the Odds be Ever in Your Favor

Odds are very similar to probability, but they are definitely 2 different animals!

Here is the equation for calculating odds:

Odds =    # of desirable outcomes  

             # of undesirable outcomes

Here is an example:

If I have a standard deck of cards and you randomly draw 1 card, what are the odds that the card is a jack, queen, or king?

First, keep in mind that a deck of cards consists of 52 cards. There are 4 coats in a deck of cards (diamonds, hearts, spades, clubs). This means that there are 4 jacks, 4 queens, and 4 kings in a standard deck.

Therefore, the number of desirable outcomes is 12 (4 + 4 + 4 = 12).

We must now determine the number of undesirable outcomes. If there are 52 cards in a deck and there are 12 desirable outcomes, logic tells us that there must be 40 undesirable outcomes (52 - 12 = 40).

So, the odds that the card is a jack, queen, or king are 12 : 40 -----> don't forget to SIMPLIFY! :)

12/4 = 3

40/4 = 10

Answer:  3 : 10

NOTE: You will often see odds records as a ratio rather than a fraction. While it would not have been incorrect to record my answer as 3/10, I prefer not to do this because I do not want my solution to be confused with probability.

I have searched tirelessly for videos or games that will help you to better understand odds. I discovered 2 things:

1) The odds of finding such things are clearly not very good.

2) Many of the sites I found were confusing odds and probability.

SOOOOOOO....

My next post is going to deal with the difference between odds and probability, how to convert probability to odds, and vice versa! Hold on to your seats!

Instead, I will leave you with this comic strip, which I found rather amusing:

So long for now!

~Tammy

More on Probability

What happens when probability becomes a bit more tricky?

One of the questions that I posed in my previous post was this:

What is the probability of landing on heads 3 times in a row on a coin toss?

Well, for complicated questions like this, I cannot stress enough how much easier it will be if you construct a probability tree diagram. Here is a tree diagram for the question above:

                                                           H = Heads      T = Tails

Each section represents a possible result from the coin toss. The first coin toss shows 2 possible outcomes: heads or tails. Of course, there is a 1/2 chance of getting either head or tails for each toss. From there, the probability tree shows the possible results of the second and third tosses.

Since our question concerns tossing heads 3 times in a row, we follow the map to view the possible outcomes of tossing heads for each of 3 tosses. Of course, each toss is independent of every other toss so the possibility of tossing heads for each individual toss is always 1/2.

To find the probability of rolling heads 3 times in a row, you simply must multiply the probability of tossing heads for each of the 3 tosses:

  1           X            1           X           1         =       1  
  2                         2                        2                  8

P = 1/8 

Here is another EXAMPLE:

You have a bag that contains 2 blue marbles and 3 red marbles. What is the probability of drawing a red marble and then a blue marble out of the bag without replacement?

Start your tree diagram by  showing the probability of first drawing a blue marble out of the bag. Next show the probability of drawing a red marble first. Your tree diagram should look like this:

Since you are not replacing the first marble you drew from the bag, your # of possible solutions will be 4 instead of 5. Using this new number, show the possible outcomes of your second draw. Your tree diagram should look like this:

 

To determine the chances of drawing a red marble and then a blue marble (in that order), you simply analyze your tree diagram. The probability of drawing a red marble first is 3/5. The probability of drawing a blue marble second is 2/4 (or 1/2). To determine your answer, just multiply these 2 values:

   3         X        1        =       3   
   5                   2                10

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While I know that tree diagrams can be a bit confusing at first, it is a problem-solving strategy that is worth taking the time to learn because it will help you immensely in the future. Click Here to access a site that has further explanations about tree diagrams and even offers you the opportunity to try some sample problems.  

Practice, practice, practice! The more you are exposed to probability problems, the more you will begin to understand them and solving these problems will become second nature!

Thank you for stopping by and enjoy the weekend!

~ Tammy 

What Are The Chances...?

 Let's start with the wonderful world of probability!



Probability can be a tricky little monster, but not if you know the steps to succeed. What is the probability of landing on heads 3 times in a row on a coin toss? What are the chances of choosing an ace out of a standard deck of cards? What is the probability that you will pull a red, then a white, then another red ball out of a bag that contains 5 red balls and 6 white balls?

I will answer these and more questions for you, but lets start with the basic.

Probability (P) =  # of desired outcomes
                            # of possible outcomes

Let's look at an EXAMPLE:

What are the chances of choosing an ace out of a standard deck of card?

# of possible outcomes: 52 (52 cards in a deck)
# of desired outcomes:  4 (4 aces in a deck of cards)

Therefore, the probability of choosing an ace is 4/52...but we much REDUCE, REDUCE, REDUCE!

P = 1/13

Let's look at another EXAMPLE:

Refer to the spinner above for the following questions:

What it the probability of the spinner landing on red?

First, count the # of possible outcomes. In this case, there are 16 possible outcomes.
Second, count the # of red slots: 6
Third, show the # of desirable outcomes (red) over the number of possible outcomes: 6/16
Fourth, simplify. P = 3/8


Now, what is the probability of landing on...

Yellow?   P = 3/16
Green?   P = 4/16 = 1/4
Blue?      P = 3/16

CHALLENGE: using the information above, can you answer the question posed in the illustration above? Look at the bottom of this post for the answer!

I sure hope that this has helped you to have a better understanding of probability. I will answer some more complicated questions about probability soon, so make sure to check in later!

Thanks for visiting!

~ Tammy

P.S. Here is a link to some fun probability games for practice:
http://classroom.jc-schools.net/basic/math-prob.html
One of my favorite games at the above link is the fish tank game. Here is a link for that game:
http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html

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So, what probability gives you the best chance on the circus spinner above? You must add the probability for each color.

Yellow or Red:     P = 9/16
Blue or Yellow:    P = 6/16
Green or Blue:    P = 7/16
Green or Red:    P = 10/16 <--------This combination will give you the best chance!

Introduction

                                         

Hello, and thank you for visiting my math blog!

I know how confusing math can be for many people, so I am here to clear up some common math mysteries and misconceptions! First, let me start by introducing myself.

My name is Tammy and I have had a love for mathematics since I can remember. It was always my favorite subject in school and I enjoy sharing my passion with others. I am currently a student and will be graduating with an associates degree in elementary eduction this summer. I will then be attending Northern Arizona University beginning in the Fall 2013 semester where I will be pursuing a dual major in elementary and special education with an emphasis in mathematics.

One of the biggest arguments that many students have regarding why they shouldn't have to worry about math always seems to be this:

"I'M NEVER GOING TO HAVE TO USE THIS AGAIN!!"

While I agree that there are some math concepts that are used more frequently than other in an average person's life, one thing is for sure:

Math teaches you how to think.

My grandfather always said that math is like exercise for your brain. It makes you think in ways that no other subject can. Math teaches you how to be a good problem solver and that is a skill that everyone will use every moment of everyday of their lives.

I believe that math has a very bad reputation and that there are far too many people who think that they simply are not good at math and never will be.

Well, I refuse to believe this myth. So, before you continue on through my blog, I encourage you to wash away all of those negative thoughts. To begin, let me make a few things perfectly clear...

You ARE intelligent.

You KNOW how to think.

You CAN solve a problem.

You CAN be good at math.

You WILL succeed.

Join me as I share many different ways that math can be fun and understandable through pictures, videos, games, and more!

Thank you, again, for visiting my blog!

~ Tammy