Bittersweet Week

So I got the call this morning, and Better Candidate outshone me again because they had more experience in a classroom setting. Tell me universe - how am I supposed to get more experience when I can't get into the classroom?

I've also been dealing with the most painful ear infection I can recall. The doctor gave me steroidal ear drops but now my ear feels like it is full of water and I would punch kittens if it would make the pain and stuffy-ear-feelings stop.

On the bright side: I got a perfect score on my first math test of the semester.

I have never received a perfect score on a math test in my life, so I'm a bit excited. Part of it I'm sure has to do with reviewing the material several times in order to teach it to other students and explain it in the blog. I also have get to start making a game for an elementary level class involving statistics. We'll see how that one goes. Now if only I can do as well on my art history exam today as I did on my math test - fingers crossed!

Odds

So I'm on a math roll today, finally got my math homework done and realized that I am one math post short for the math blog - oops! So I'll be covering the last and shortest part of the probability section: Odds!

Now, odds and probability are different, and it is important to know what that difference is.

Image from Math Magic website

The numerator for both is the amount of times you obtain the desired outcome, but the difference lies in the numerator. While probability has a denominator that lists all the outcomes, when calculating odds, you have the undesirable outcomes as your denominator.
To find out what the undesirable number is, simply find the total number of outcomes and subtract from that the number of desirable outcomes. This leaves you with the undesirable outcomes, your odds denominator.

Math Magic has a great page explaining probability and how to change from probability to odds. See it here: Math Magic - Probability

Probability (Part II)

I began writing this post a week ago and forgot to publish it! I could kick myself :P

Let me start with this: Tree diagrams are not my friend. They confuse me to no end and I couldn't tell you why, they just do. So when we began our probability section, and tree diagrams were introduced as the way to record information I just about lost it. It took me three lectures for it to click, and even now I couldn't explain it to with total confidence, but here we are. Geronimo!

Multistage Experiments with Tree Diagrams

• One-stage experiment - experiments that are over in one step.
• Two-stage experiment - Ex.: a ball is drawn from a box, and recorded in the same way as in the one stage experiment; then the ball is replaced, and a second ball is drawn and its' color recorded. 

Now, tree diagrams are used to record the results of these experiments using visual representation in lieu of boring old data tables. When recording and performing there are two types: with and without replacement. They are exactly as they sound - in one you perform the experiment and replace what was removed, and in the other you don't.

"Pom Pom" experiment showing probabilities
both with and without replacement.

Above is one such experiment, using puff/pom pom balls. In a box we have 3 balls, two white and one black. The probabilities are calculated based on the ratios: 2/3 of the balls are white, 1/3 are black. Depending on whether or not we replace the balls after pulling them from the box changes the probability of drawing that color next. We determine that probability by multiplying the ratios.

Another example is shown here:

The first example shown in the image illustrates another probability concept using the word PROBABILITY itself. It demonstrates the probability of spelling the word BABY, with the letters drawn in the correct order, both with replacement of the letters and without replacement. Again, we multiply to find the probability.

The second example uses the same idea, only using the word RANDOM to spell DAN. Again this shows both with and without replacement.

So we've been talking about probability, but what is it?

So probability is fractions (kind of), which may explain why I've had so much trouble - fractions are not my friends.