Friday, May 18, 2007

LONG Weekend = LONG Scribe

This class was the second one of the unit of PROBABILITY. That is, as Grey-M stated in the last scribe post, the easy unit of PROBABILITY, but anyway...

...The class started with the student elections. 3 of the 4 candidates for the executive council were in our class so it was a fairly bid deal. (To see the results, check the post prior to this one by Sandy.)

After that, we reflected upon the extraordinary video display by Richard in the previous day's candidates' speeches. We liked it so much in fact, that we searched YouTube for it. We didn't find it, so instead we watched a video that was completely irrelevant to math, or anyone in our class for that matter =D.

Then, we got down to some "ACTUAL MATH!"

The first slide shown was a little too easy I believe, but Mr. K. didn't find it as such (haha!)
Then, Mr. K presented us with on that was a little higher on the difficulty scale. We were to "TEST THE QUESTION FOR INDEPENDENCE".
We'll take a quick trip back and review exactly what an independent variable is:
Thank You Grey-M! =)

Now, to test a question such as:

30% of seniors get the flu every year. 50% of seniors get a flu shot each year. 10% of seniors get the flu even though they've had a flu shot. Are getting the flu and getting a flu shot independent events?

•The first step is to look at the set. (In this case it is the SENIORS)
•Next, identify the categories. (Whether they GOT THE FLU SHOT or NOT)
•Now, we identify what event can occur to each category. (they can GET THE FLU or NOT)
• The fourth step in the solving in this problem is to draw a tree diagram:
•Now we can write in the probabilities of each event.
•Then, find the favourbale outcome, or the outcome which we want.
•Now just calculate the probability of the favourable outcome and compare it to the given percentage:
Here we see that the probability of catching the flu and getting a shot is not 10%, it is 15%. This means that they are not independent events.

Next, we moved on to questions that dealt with events that were "MUTUALLY EXCLUSIVE". This means that it is a situation in which one(or more) of the outcomes of the event becomes impossible if the other(s) is(are) chosen.
If Mr. K. were to pick from the class one boy, he will not be a girl. If he picks a girl, she cannot be a boy.
An event can be determined to be mutually exclusive (or "disjoint") if the probability of getting both outcomes is zero(Ø), also known as an empty step.
**both events would be written as "A", "(upside-down U)", "B".**

After that we did problems that asked for the probabilities of "AUB" (A or B). If it is mutually exclusive, then simply add the probability of "A" and the probability of "B".
However, if it is not Mutually Exclusive, we must also subtract the probability of "A and B", because it is not A OR B if both are chosen:
We continued the class by doing more questions dealing with "AND" and "OR" and finished off with a couple situations for which we had to decide whether it was either:
This can be found in the slides (2 posts previous to this one).

To finish off:
•Hope everyone's Long Weekends were better than mine.
•Enjoy your day off =D