What are the Odds?

When I think of Odds I always think of Gambling so I thought this picture did that justice.

FINDING THE ODDS

Odds are used to describe the chance of an event occurring. The odds are the ratios that compare the number of ways the event can occur with the number of ways the event cannot occur.

The odds in favor - the ratio of the number of ways that an outcome can occur compared to how many ways it cannot occur.

Odds in favor = Number of successes: Number of failures

The odds against - the ratio of the number of ways that an outcome cannot occur compared to in how many ways it can occur.

Odds against = Number of failures: Number of successes

Example:

A jewelry box contains 5 white pearl, 2 gold rings and 6 silver rings. What are the odds of drawing a white pearl from the jewelry box?

Number of successes = 5

Number of failures = 2 + 6 = 8

Numbers of ways to draw a white pearl: number of ways to draw another jewelry.

5:8

The odds are 5:8

Simulations in Probability

Simulation is a way to model random events, such that simulated outcomes closely match real-world outcomes. By observing simulated outcomes, researchers gain insight on the real world.

Why use simulation?

Some situations do not lend themselves to precise mathematical treatment. Others may be difficult, time-consuming, or expensive to analyze. In these situations, simulation may approximate real-world results; yet, require less time, effort, and/or money than other approaches.

How to Conduct a Simulation

 Courtesy of Sophia Learning I found a great video to show this. 

Multistage Experiments with Tree Diagrams

Calculating probabilities can be hard, sometimes you add them, sometimes you multiply them, and often it is hard to figure out what to do ... tree diagrams to the rescue!

You can use Tree Diagrams for either an Independent Events or Dependent Events.

Independent Event: When the occurrence of one event has no influence on the outcome of a second event. An example of 2 independent events are; say you rolled a die and flipped a coin. The probability of getting and number face on the die in no way influences the probability of getting a head or a tail on the coin.

Dependent Event: The outcome of the event affects the second event. I found a great example of this on  wyzant 

For example, if you were to draw a two cards from a deck of 52 cards. If on your first draw you had an ace and you put that aside, the probability of drawing an ace on the second draw is greatly changed because you drew an ace the first time. Let's calculate these different probabilities to see what's going on.

There are 4 Aces in a deck of 52 cards

On your first draw, the probability of getting an ace is given by:

If we don't return this card into the deck, the probability of drawing an ace on the second pick is given by

As you can clearly see, the above two probabilities are different, so we say that the two events are dependent. The likelihood of the second event depends on what happens in the first event.

Here is a great video of showing how to use a tree diagram for finding the Probability of 4 different situations.

It really helps having a visual of what you are trying to find instead of just doing the work in your head. 

Probabilities and how they are determined.

To be honest I was totally lost when we started this section. I thought I knew everything that was needed to be known about Probabilities that I needed to know. But reading about it and knowing it are 2 different things. I am a visual learner so I need to have pictures and actually things in front of me to learn. So while reading about all the terms Experimental prob, theoretical, equally likely, uniform sample space, I was totally zoned out. trying to figure out what our teacher was talking about.  But then we started some activities such as Probability of using cards. Such as this Video explains.

I started to get it a little better. But I still was struggling a little until we did an activity the colored goldfish crackers. I had the crackers in front of me and I could physically see the difference. Then it clicked and I knew i got it!  I found a great web site that gives you vocab and an example of what they mean by that definition. Also some Practice questions from Math Goodies

Starting a Blog.

I would normally never do something like this, but for a good grade I will do about anything.

My name is Amanda Brockmann and I am studying to become a Preschool teacher. I have always loved little kids and am a natural as some people will call it with playing and teaching children. My plan for the future is to open my own Preschool within my own home so that i can be home if my own children need me.

I have been married for almost 4 years now to the Love of my life Jacob. We are expecting our first child this July and we both are a little nervous to be completely honest.  We get to find out the Sex of our Little one on Valentines Day! I can't wait. Jacob swears we are having a boy so there is no reason to go find out, but to just bug him I tell him we are having a girl. ;) We have lived in 3 different states in our years of marriage. Utah, California, Washington and Now Arizona. We both were born and raised her in Mesa and we are glad to be back. I was tired of moving from state to state.  It was very hard to try to continue school while moving around. I would sign up and get registered then we would move. So I did not get very far in my education plans while moving around but now that we are not planing on moving for a while... at least till Jacob is ready to go to dental school. This is my last semester at MCC and then I am going to NAU at the Chandler/Gilbert campus.