<body><script type="text/javascript"> function setAttributeOnload(object, attribute, val) { if(window.addEventListener) { window.addEventListener('load', function(){ object[attribute] = val; }, false); } else { window.attachEvent('onload', function(){ object[attribute] = val; }); } } </script> <div id="navbar-iframe-container"></div> <script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script> <script type="text/javascript"> gapi.load("gapi.iframes:gapi.iframes.style.bubble", function() { if (gapi.iframes && gapi.iframes.getContext) { gapi.iframes.getContext().openChild({ url: 'https://www.blogger.com/navbar.g?targetBlogID\x3d15925399\x26blogName\x3dPre-Cal+40S+(Winter+\x2706)\x26publishMode\x3dPUBLISH_MODE_BLOGSPOT\x26navbarType\x3dBLUE\x26layoutType\x3dCLASSIC\x26searchRoot\x3dhttp://pc4sw06.blogspot.com/search\x26blogLocale\x3den_US\x26v\x3d2\x26homepageUrl\x3dhttp://pc4sw06.blogspot.com/\x26vt\x3d8544817652058964798', where: document.getElementById("navbar-iframe-container"), id: "navbar-iframe" }); } }); </script>

Tuesday, May 02, 2006

Jefferson's Scribe - Introduction to Probability

大家好(hello everyone), my name is Jefferson, thanks to Janet I am the scribe for today. Today Mr K started us off with some questions on the board. The first one went something like this:
a)


How many ways can you get from A to B by the shortest route possible? (i.e. only moving right and down)
There are many routes to take that are short. And out of all the shortest routes you can think of to take, they all end up 4 blocks to the left and 3 blocks down.


And resulting in "RRRRDDD". With this we were able to figure out a solution for this question. Manny came up to the board and explained to us that this question is similar to out "MISSISSIPPI" problem. Since there are 11 letters in mississippi,4 "S"s, 4 "I"s and 2 "p"s, we plug those numbers into the "permutations of non-distinguishable objects" formula n!/(k1! k2! k3!). And it will look something like this:

11!/(4! 4! 2!).

SOOOOOOO back to our original question. There are 7 letters in (RRRRDDD), 4 "R"s and 3"D"s, lets plug them into the formula and see what happens!!!

7!/( 4! 3! ) = 7 * 6 * 5 * 4 * 3! / (4 * 3 * 2 * 1)3!

7!/( 4! 3! ) = 7*5

7!/( 4! 3! ) = 35

*"3!" get cancelled out

*4 gets cancelled out

* 6 / 3 = 2

* 2 / 2 = 1

So there are 35 ways to get from point A to point B.

And the next question had a similar diagram:

b)
To find the solution we had to find the number of was to get from
point A to point a, point a to point b, and point a to point B.

A-a : RRDD 4!/(2!2!) = 6

a-b : Rd 2! = 2

b-B : RRRRDDD 7!/(4!3!) = 35

6 * 2 * 35 = 420 ways

Mr K then showed us another way which he liked to call "The inside secrets of the universe".

a)

Do we all know why there are a bunch of 1s at the top and left? Because from point A there is only one way to get there.

By adding the top right corner and the bottom left corner of a single square, you'll get an answer for the bottom right corner of the square. And that answer determines how many ways are possible coming from point A to that bottom right corner. In this case : 1 + 1 = 2. Our bottom right corner is 2 and that means there are 2 ways that point(2) from point A.

And by adding all the corners until you get to the last corner of the entire diagram. The answer is 35!! Just like our first solution!

And for the next question:

b)

The answer is also 420!!

The method that Mr K showed us was called "Pascal's triangle" Which is used everywhere!!

And the next and final question:

Write your answer to this question as a fraction only. Do not discuss with neighbor.

What is the probability that the sky will fall?

The solutions that most of the class answered were the following.

1/(10)^10^100 ' 1 out of googolplex things that could happen

o / ∞

0/1

0/0 (4 students answered) 'means that it is impossible to happen

1/2 (3 students answered) '50% chance of it happening

1/6

1/ ∞ (3 students answered) '1 out of infinite things that could happen

1/ 10^10^12 '1 out of a trillion things that could happen

1/1000000

The formula for this sort of question would be:

# of favorable outcomes/everything that could happen

And the solution is that the sky is undefined

The reason why Mr K gave us this question was to illustrate the concept of a sample space

If you were to flip a coin, the probability of getting heads or tails is 2. If you were to flip the coin again the probability 2 again. This is explained by this tree diagram

This is an easy way to find the probability of a coin

If you were to roll a six sided die the chance of getting a 6 is 1 out 6 chances and 0 out of 6 chances of getting a seven.

If you were to roll 2 dice you would get 1 out of 36 ways of getting a number.

This chart illustrates the probability of getting any number from rolling 2 dice

i.e there are 6 chances of rolling a five.

Homework is on p 371 of the text book # 1-13 (all)

WOOOOO I'M DOWN!!! This took me about 4 hrs to finish this scribe...man talk about dedication...hah I'm kidding! Now, the next scribe is non other than.... MARK!!LATER DAYS, SCRIBE SPECIALIST!!!JEFFERSON!!!


再見(goodbye)



Français/French Deutsch/German Italiano/Italian Português/Portuguese Español/Spanish 日本語/Japanese 한국어/Korean 中文(简体)/Chinese Simplified Nederlands/Dutch

6 Comments:

At 5/02/2006 8:36 PM, Blogger Jefferson said...

this took way too looooong............*fainted*

 
At 5/02/2006 9:13 PM, Blogger Mr. H said...

This is the third scribe for your class that I have read today. It is really well done. As with the others I am amazed at how much informations is in your scribe. The examples you give are great teaching tools in explaining the concepts of the day. The rolling script at the bottom is a nice new feature.


Great Work

Mr. Harbeck
Sargent Park School

 
At 5/02/2006 9:52 PM, Blogger Mr. Kuropatwa said...

Wow Jefferson! I really liked that you included and translated the chinese text. ;-) Great graphics and detail in the description. I don't normally like to see "marquee" text, but I liked the way you used it.

I'd say the New Emperor has begun his dynasty. ;-)

BTW, the question about the sky falling was to illustrate the concept of a "sample space."

 
At 5/03/2006 12:48 AM, Blogger Regine said...

EH. YOU'RE GETTING TOO MUCH PRAISE. AND YOU KNOW WHAT! haha. i'll give you more praise. nice work, guY. haha. i liked the last part where it's a bit flashy and stuff moves around.haha. you suck up... =D

 
At 5/03/2006 8:57 AM, Blogger Lani said...

Hi Jefferson,

Your four hours of hard work surely did pay off!! Seems to me you found you had a second wind and really exceeded all your own expectations!! Congratulations!!

Just a thought: I wondered about a Scribing Hall of Fame to which everyone could aspire. It seems to me that you, Janet and Michael should be the initial inductees. You have set such high standards!! Maybe the members of the Hall of Fame could even have mention of their membership in their profile image.

Again, congratulations on such good hard work!!

Best,
Lani

 
At 5/03/2006 8:30 PM, Anonymous Graham Wegner said...

I know it's been said in your comments before but I can really use your scribing example to inspire my much younger students to get into Maths (Australian abbreviation) when they hit high school. Great work!

 

Post a Comment

Links to this post:

Create a Link

<< Home