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.