Probability

Sample Space -can be defined as any complete and total representation of the outcomes in a probabaility situation.

Ex. Roll a regular 6 sided die; spin a spinner (numbered 1-4).

Represent/show/display/sketch…. “The sample space”
6x4=24 possible out comes in the sample space.

The sample space is:
(1, Green) (1, Red) (1, Orange) (1, Blue)
(2, Green) (2, Red) (2, Orange) (2, Blue)
(3, Green) (3, Red) (3, Orange) (3, Blue)
(4, Green) (4, Red) (4, Orange) (4, Blue)
(5, Green) (5, Red) (5, Orange) (5, Blue)
(6, Green) (6, Red) (6, Orange) (6, Blue)

Everything and al possibilities are displayed

Mutually Exclusive and Mutually Inclusive Events

mutually exclusive events CANNOT occur together

ex:

Events A and B are mututally exclusive, they are disjoint sets. ( they have no common members)

The following formula is the only formula to be used with mutually exclusive events ONLY!

P(A or B)= P(A) + P(B)

ex: What is the probability in a regular deck, on a single card flip, of drawing a face card or a 5?

A: face card

B: 5

P(A or B)= P(A)+P(B)
P(f or 5)=P(f)+P(5)

=12/52+4/52
=16/52
=4/13 or 31%

Mutually inclusive events DO happen together

ex:

A:face card- 12/52
B: red cards-26/52

38/52 is WRONG

because you cannot count them twice!!

the correct way to do this is:

P(AorB)=P(a)+P(B)-P(A and B)

=12/52+26/52-6/5

=32/52 or 8/13 or 61.5%'

*use venn diagrams* put examples of mutually inclusive and exclusive events venn diagrams

the above are venn diagrams of the two examples given earlier.
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INDEPENDENT/DEPENDENT EVENTS
*involves chronology of events(order in time)

Independent events do NOT have an effect on each other (ie. successive coin flips)these events are random.

Dependent events do have an impact on some subsequent probability event (ie. newest thing Depends on an older thing) these are not random.

example of dependent events

ex: "with or without replacement"
socks from a drawer
balls from an urn
Take for example the famous game off of "The Price Is Right" 3-Strikes game.

Fundamental Counting Principle:

When order doesn’t matter you use nCr. You enter the first number (number of letters in the alphabet, number of 5 cards poker hands, etc…), press math, PBR, nCr, the second number (the number of letter code words/the number of diamonds and hearts, etc…).

When order does matter you use nPr. You enter the first number (number of letters in the alphabet, number of 5 cards poker hands, etc…), press math, PBR, nPr, the second number (the number of letter code words/the number of diamonds and hearts, etc…).

Compliments:
A'=(1-A)
A+A'=1

The definition of A is one thing or one sample. The definition of A' is everything else involved except A.

Pascal's Triangle:

Starting at the house CO-OP you head home but have to stop at Bob’s house to pick up your homework. You can only head South and East. How many ways can you get home from the CO-OP while stopping at Bob’s house?

Imagine encountering a problem like this…DON’T RUN AWAY IT’S EASY!!
You use Pascal’s Triangle. You first figure out the larger rectangle then the square.

You start off by adding the two ones to get 2. You then add the next one on the side and the two you just got to get three, you continue by adding the two numbers beside each other and putting their sum in the box below UNTIL you reach the red square, this is the stop point. You then start again in the new square and stop at the stop point.
You then add the two numbers that are in the red boxes, which are 126 and 6.
126+6=132

So therefore there are 132 ways to get from CO-OP to Home.

What I Think I'm Supposed To Have Learned...or Mentoring 101

At the end of our section on Matrix Modelling, I am confident (no, really, I AM confident), that my students here in Swan River will be more than capable of teaching their peers in Dauphin some of the finer points regarding what we've covered so far.

Specifically, what they'll be doing (or what you'll be doing, if you happen to be unfortunate enough to have landed on my class list this semester), is this:

photo credit: http://www.svleck.com/images/helping%20students%20stat.png

1. In your Blog Team, begin a series of posts describing the 'ins and outs' of one sub-topic in the unit on Matrix Modelling. I'll tell you in class who your team is, and what your sub-topics are.

2. Your language is critical to the success of such an experiment. You need to talk on the blog like a high school student speaking with another high school student (whom you don't know), since that is exactly the situation that we're in. Grammar, spelling, and punctuation are really important, since you don't know whom you're speaking to, and the only thing that they have to base the quality of your instruction on is your language....Having said that, I think a sense of humour is really worthwhile, as is the sense that the world is much larger than our small piece of geography in the Parkland...

3. I hope that it's obvious that I expect you to post screen shots, recordings, external links, etc....including anything and everything that might help the students in Dauphin learn what you're supposed to know...Be creative, and think carefully about what you're posting...

Rationale: Am I expecting my students to 'create' learning opportunities for other students in other communities, just because? Believe it or not, I'm not really that crazy about 'busy work'....Teachers as well as students are busy, and need to trust that their time is well spent in learning environments/opportunities....So here's my take...(and I take absolutely no credit for this idea, it's just 'common' knowledge, especially to first-year teachers)....

"Having to teach something to someone else
makes you learn it yourself, really, really, well...."

....which I hope does a quick job of explaining at least one of the reasons why we're doing what we're doing....

RM