Probability-Sample Spaces and Complimentary Events

Sample Spaces-any complete representation of all probability outcomes in a probability experiment(some measurable event)
Examples of sample spaces would be coordinate points, tree diagrams, charts, words saying each possible outcome.

Complimentary Events- P(A)+P(A)'=1
This means the "probability of event A" +"Not the probability of event A" =100%

Factorial Notations-Into Perms&Coms

Permutation- an ordering of objects in which order matters.
Combination- an ordering of objects in which order doesn't matter.
*The exclamation mark is "factorial"*

Perm VS. Com
We did examples to show the differences between Perms and Coms:

1- How many 5 letter "words", using the alphabet, no repeats?
26*25*24*23*22=7893600
26!=(26*25*24*23*22)*21!
SO 26*25*24*23*22=26!
21!
Divide it by 21(the 6th number) because there are only 5 spaces for the letters to go into.
You can do this on the calculator with this equation:
nPr= n!
(n-r)!
SO 26P5= 26!
(26-5)!
=7893600
Part 1 is a permutation because the order of the letters matters since there are no repeats.

2-How many poker hands are there with hearts/diamonds only?
There are 26 hearts/diamonds alltogether in a 52 card deck, so we go like this:
26*25*24*23*22 = 7893600 = 65780 unique poker hands using hearts/diamonds only.
5 * 4 * 3 * 2 * 1 120
You can do this on the calculator with this equation:
nCr= n!
(n-r)!*r!
SO 26C5= 26!
(26-5)!*5!
The extra *5! is to divide out all combinations with the same 5 elements(the same 5 cards, but in different orders)
Part 2 is a combination because the order doesnt matter.

Probability-Fundamental Counting Principal

F.C.P.-Fundamental Counting Principal

**...if you can do event A in a ways, and B in b ways, etc... then the number of ways to do event A, followed by number of ways to do event B, etc...**

This means: Number of ways to do A, B, C, ....=a X b X c....

Probability Intro..

Yesterday we did our Probability introduction and I was the class blog scribe. All the information is on that blog, with pictures too.

Vector "tricks"

Yesterday Mr.Max showed us some Vector templates.
To open them you have to first open Euklid, then get to the "stuff you can use on your exam" folder.
In that folder there are 2 templates, one is the Triangle Method, and the other is the Parallelogram Method.
For each method you can move the 2 vectors to where they are supposed to go and to what length to calculate the resultant vector.

Vector Exercises

Yesterday we just had a work class. We worked on the exercises 1-4 some more.
Here are some pointers:
For the triangle method, the tail is stacked onto the head of the previous vector.
For the parallelogram method, the tails are placed on the tail of the other vector.

Parallelogram Method

Parallelogram-a 4 sided polygon with opposite sides parallel.
We use the parallelogram method when there are situations with simultaneous vector addition, NOT stacked/chronological order.
Steps:
1)Create V1 with the tail on the origin
2)Create V2 with the tail on the origin.
3)Create 2 parallel sides to make a parallelogram
4)Create the resultant vector starting from the tail of V1 and V2(the origin) to the intersection of the parallel sides

Vectors Project

Nov. 10/09
We were given a vectors project that is due on November 27th at 4:00 p.m.

The project includes:

-Starting with a known resultant vector

-5 scenarios that have their answer as the resultant vector.

-Each scenario has to have a minimum of 2 vectors(with magnitude and direction scaled for each)

-Title page, table of contents, intro, references(if any), discussion(if any), conclusion, *diagrams

*Format is negotiable*

Vector Addition

We started vector addition today. These are the steps for the triangle method:

1-Starting from some origin, create a vector(to scale), that has the tail on that origin

2-From the head of the original vector(v1), square it(make another origin) for measurment.

3-Create V2, V3, V4, etc... and "square up" each vector head for measurment.

4-Create the resultant vector from the origin(starting point) to the head of the last "added" vector.

*Resultant vector is a vector from the tail of the original vector(origin), to the head of the last added vector*

We did an example on Euklid, and to "square up", in the construct tab there is a "parallel" button. Click that, then click the point you want to square up(the head of the last vector), then the X or Y axis to make it parallel.

Vectors on Euklid

Today Mr.Max showed us how to do vector questions on Euklid. It's actually really simple, and way faster than how I did it in Physics last year. All you have to do is make a fixed length line segment(to scale, with the scale legend typed onto the graph), and then measure the angle from a point on the axis, to O, to the end of the vector. To switch the line segment into a vector, you hit the vector button, then click on the ends of the line in the direction that it is going.
And that is pretty much all that we did today. Exercise 2 of the vectors booklet given to us yesterday is due on Thursday, not tomorrow because we have our first grad meeting tomorrow during block 1.

Vectors!

Today we started off on the Vectors unit. We learnt how to use the Euklid program, how to make lines with a fixed measurement, and measure angles. Once we finished that lesson we were given a Vectors exercises package to work on. We should be done the unit by next week.