It's almost here...

I can't believe that our class journey is ending today. It seems like yesterday I was trying to remember your names. As I'm writing this scribe, the countdown to the final installment of the Pre-Calculus 40s is showing less than 100 hours. I believe that you will succeed. I wish you all the best on the exam and in your future endeavors. It was my pleasure to have you as my students, to learn with you the language of math, and to know you.
Mr. P

Probability

P (E) = Success/Sample Space
Sample Space
A sample space is basically all possible outcomes. Some ways used to illustrate sample space are:
         - Tree diagrams



       
          - Ordered pairs
      {(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)}
Independent events are when two events occur at the same time that does not affect the probability of the other.
                EX. Picking marbles and rolling a dice.
Dependent events are when two events occur that does affect the probability of the other
                EX. Taking gum from a gum ball machine without replacement.

Example: A jar has 16 green marbles and 5 red marbles. If one marble is pickd from the jar what is the probability that it will be red?

P (E) = Success/Sample Space

p (E) = 5/21

Unit 6 and 7 test

HEy,
Mr.P I am ready for test tomorrow

Unit 6/7 Test

Hey Mr.P, i'm ready for the test.

Probability using Permutatins and Combinations

Permutation-set of items selected and arranged-order matters
Combaination-set of items selected-order does not matter

Here have some examples for Probability using Permutations and Combinations:

Example 1) Aclass consists of 10 men and 8 women. Four members are to be Selected( mean use Combination to calculate this question) at random to represent the class. What is the probability that the selection will consist of two men and two women?
P(two men and two women)
=10C2x8C2/18C4
=1260/3060
=0.14

Example 2) If the letters in the word CALCULUS are arranged ( Premutation) what is the probability that...
a) the C's are together
P(C's are together)
=(7! 2!/2!2!2!)/(8!/2!2!2!)
=1/4

b) the C's are apart
P(C's are apart)
=1-1/4
=3/4

Conditional Probability

Conditional Probability means that the "event" has one or more conditions, which are restrictions.

Events with one condition involve finding the probability of a specific item.

To solve this you multiply the probability of the location of the item by the probability of the amount of specific items in its location.

Example 1: There are two bags. A coin is flipped to determine which bag to draw from. Bag #1 contains 4 basketballs and 2 footballs. Bag#2 contains 10 basketballs and 2 footballs. A ball is drawn at random from the chosen bag. Find P(Basketball).















Events with two conditions involve finding the probability of obtaining a specific item and it must come from a specific location, which leads to a reduced sample space.

To solve this type of question you use the equatoion:









Example 2: Using the same items in example 1, find P(Bag#1/Basketball).






















and THAT, is how it's done ..

Hey Mr.P

Could you upload the rest of the probability notes? I think im missing a couple pages.

Thanks

Geometric Seris

Hey Mr. P
Can you just tell me how the Sigma notation works  in the geometric series. How do we use the formula to evaluate.

Homework over holidays

Hey Mr.P, what exactly should we have finished for school on thursday, because it seems like i am missing a few pages or exercises for some reason.

MERRY CHRISTMAS