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Thursday, February 23, 2006 

Scribe February 23, 2006

Hi, for today's class we've study about the amazing Pascal's triangle or also called as The Precious Mirror of the Four Elements. What's amazing in this triangle is it can give a lot of information, for example, the answer to the number to the power of 2 it can be found by adding all the numbers every row. Also the number 11 to the power of 1,2 ,3 , 4 and so on it was exact number in every row of the triangle like 11 to the power of 0 is 1, 11 to power of 1 is 11, 11 to power of 2 is 121, 11 to power of 3 is 1331 and so on. We can also find triangular numbers, natural numbers, hexagonal numbers, pentatope numbers, fobonacci number, catalan numbers and tetrahedral numbers. here is how Pascal's triangle looks like
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
The next row can be found by adding the numbers in between from the last row of numbers and the next row must be begins and end with number 1. So the next row of the triangle above would be 1 7 21 35 35 21 7 1 and the process continue forever....
For those who missed the class here are the notes
PROBABILITY: The branch of mathematics that deals with chance
SAMPLE SPACE: The set of all possible things that can happen for a given set of circumstances
example: rolling a die-6
sample space would be (1, 2, 3,4,5 and 6) because this is all the possible outcomes
EVENT (E): An event is a subset of the sample space. It is one particular outcome for a given
set of circumstances
SIMPLE EVENTS: The result of an experimental carried out in 1 step
example: flip a coin. The result is Head
COMPOUND EVENT: The result of an experimental carried out in more than one step
example: Flip a coin and roll a die. The result is head and number 6
CALCULATING THE PROBABILITY OF AN EVENT......FORMULA:
P(E) = NUMBER OF FAVOURABLE OUTCOMES divides by
THE NUMBER OF POSSIBLE OUTCOMES (SAMPLE SPACE)
PROBABILITY CAN BE EXPRESSED AS:
  • A ratio
  • A Fraction
  • A decimal
  • A percent
CERTAIN EVENTS: An events whose probability is equal to 1.
IMPOSIBLE EVENTS: An event whose probability is equal to 0.
IMPORTANT: Probability is always a number between 1 and 0.
FUNDAMENTAL PRINCIPLE OF COUNTING:
If there are M to do a first thing and N ways to do a second thing, then there are M x N
ways to do both things.
Example:
How many outfits can be made from 3 pants and 4 shirts?
solution: 3 pants x 4 shirts = 12 different outfits
NEW CALCULATOR TECHNIQUE:
This is use to experiment something using a calculator.....
Experiment the probability of getting exactly 2 heads on fliping 3 coins 30 times
We knew that the theoretical probability is 3/8 so here is how to do the experiment on calculator.
Step
  1. Press math button on Ti83 calculator
  2. Select probability
  3. Select randBin (random binomial experiment)
  4. type in (1, 3/8, 30) 1 represent success, 3/8 represent theoreticall probability and 30 represent number of times it was done
  5. Press enter and a result will show in row
  6. press STO butoon to store the result
  7. press 2nd function STAT
  8. Select MATH then Sum
  9. this is to get all number 1 or the success

for next scribe Rein




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