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Friday, May 05, 2006

Scribe Post: Probability is 1 out of 2 times fun for me

Hello everybody, my name is Manny and I’m your scribe for today courtesy of the newly famed Teddie. Today was pretty straight forward, it was a 2 period. The big counting test in the morning, followed by lots-a-notes in the afternoon. The test was pretty difficult, and I realized few questions I solved incorrectly as soon as I walked out of the door. It really is a bummer. I hoped you guys had better luck with it than I did. Anyway, I‘ll try to live up to you admired hall of famers. And here I go…!

In the afternoon class, we were given a huge amount of notes to absorb, with the explanation behind it of course. Probability is pretty tough for me for some reason. I’ll try to break it down, and explain it into more easier terms to make the notes more understanding by throwing in some words and sidenotes.

Let’s get started with some terminology of probability.

Certain Event: An event whose probability is 1.

Impossible Event: An event whose probability is 0.

Important: Probability is always a number between 0 and 1.

Complimentary Event: The compliment of E is E′, the set of outcomes where E does not occur (sidenote: the means prime)
If P(E) = a then P(E′) = 1 - a

Example:
The probability of drawing a spade from a standard deck of cards is
P(S)= 13 / 52
= 1 / 4
(sidenote: 13 = # face values in a standard card deck of 52)


The probability of not a spade is
P(S′)= 1 - 1 / 4
= 3 / 4


Dependent Events: Two (or more) events are dependant if the probability of the second event depends on what happened in the first event.

Example: A bag has 3 red and 3 blue marbles. A marble is drawn and not replaced. What is the probability that the second marble is blue?
It depends on what the first marble was.


Independent Events: Two (or more) events are independent if the outcome of the second event is unaffected by the outcome of the first event.

Example: Given the same bag of marbles. A marble is drawn and replaced. What is the probability that the second marble is blue?
Since these events are independent, the sample space is unchanged. The probability remains the same:
P(B)= 3 / 6
= 1 / 2


Mutually Exclusive Events: Two (or more) events are mutually exclusive if they have no events in common. I.e. They have no intersection (meaning the circles don't overlap eachother).

Example:


Calculating Probabilities using “AND” and “OR”
Given 2 events A and B
P(A and B) = P(A) · P(B)
If the events A and B are independent.

If A and B are dependant, then
P(A and B) = P(A) · P(B | A)

P(B | A) means “ the probability that B will occur given that A has already occurred.

Note: Tree diagrams are very helpful in solving these types of problems.

Examples: A bag contains 3 red & 3 blue marbles. Two marbles are drawn.

Independent Events:
Find the probability that the 2nd marble is blue if the first was red and had been replaced.


Dependant Events:
What if the first marble was not replaced?


P(A or B) = P(A) + P(B) - P(A and B)
When the events A and B are mutually exclusive P(A and B) always equals to zero. (There is no intersection/nothing in common) which simplifies to the formula above to
P(A or B) = P(A) + P(B)

Example: Flip a coin twice. What is the probability of getting two heads or tails?


So that’s all that happened in class. And to everyone in our class, the online quiz on quizstar is not going to be worth marks. Mr.K told me after class and decided not to, as the highest mark was only 50%. Yeah, I am just as surprised as everyone. If you’re curious to see what the answers are (with my explanation), you can click here.

Okay guys. It’s time for a wrap. The next scribe will be abr13l. No drum rolls, no flashy text, no cheerleading, I try to be as direct as possible ;). Homework is on page 380 in our blue textbook, questions 14-20. See you Monday guys.



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4 Comments:

At 5/06/2006 1:23 PM, Blogger Mr. H said...

The standard seems to be set in this classroom. All of the scribes over the past week have been excellent.

The content was easy to read and understandable. These scribes would be an excellent resourse to anyone taking math through correspondence.

Keep up the excellent scribing

 
At 5/07/2006 9:20 PM, Blogger Mr. Kuropatwa said...

WOW! A run of SIX Hall of Fame-ers! (Y'know, 6 is my favourite number. ;-))

Manny, as you wrote at the end, no flash or cheerleading, but, WOW, that was really fantastic. Excellent graphics and your additional annotations really help to make the material clear.

I've got to tell you, that last link in your post really knocked my socks off!

BRAVO! And welcome to the The Scribe Post Hall Of Fame. ;-)

(We really need a badge.)

 
At 5/08/2006 10:00 PM, Blogger Karl Fisch said...

Congratulations to all the scribes - you've been doing some excellent work lately (and maybe helping me convince the math teachers at my school to try having scribe posts).

I have a question for all the scribes: I was wondering what software you are using to generate the math symbols, equations, etc. in your scribe posts? I can tell that you are creating it and saving it as an image, then uploading the image to Blogger, but not what software you are using. About the only thing that we have (that I know of) that could do something similar would be using the equation editor in PowerPoint, and then saving the slide (or just the equation) as an image, but that's pretty clunky. Do you have any software you can recommend (preferably free)?

Also, I notice you often use tables to put borders around items - are you generating the HTML by hand for that, or using something else?

Any ideas you are willing to share would be appreciated. Keep up the good work - you are setting a great example not only for other students around the world, but for their teachers.

 
At 5/12/2006 7:38 PM, Blogger Lani said...

Hi Manny,

I found your use of borders on the equations and red font for the "examples" really helpful as I read your post!

And I like "direct"!!!!

Congratulations on your induction into the hall of fame!

Best,
Lani

 

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