Chapter+Three+Statistics+Notes

=Chapter 3 Notes - Probability Chapter= = = =toc= =Chapter 3.1 Notes=
 * Noah - page 128-129 (thank you)

Probability Experiment is an experiment specific results are obtained. Outcome - The result of a single trial Sample Space - the set of all possible outcomes Event - a subset of the sample space

http://www.mathgoodies.com/lessons/vol6/intro_probability.html

media type="youtube" key="1gV8LXjzE6w" height="315" width="420"

Fundamental Counting Principle: Used for: When an event can occur in many different ways that you can't write all of the outcomes.
 * Alexia - page 130


 * Jun - page 131 and 137 (pretty please:-))
 * Lukas - page 132

TYPES OF PROBABILITY:
Classical or Theoretical Probability: "The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible."



http://www.youtube.com/watch?v=n7dpXvbtZOo
 * ==== Shun - Page 133 ====
 * **Finding Empirical Probabilities**: Empirical or statistical probability is based on observations obtained from probability experiments. The empirical probability of an event E id the relative frequency of even E.

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 * **Empirical Probability Formula **

Subjective Probability: Results from intuition, educated guesses and estimates. (ie: the percent chance a patient will fully recover)
 * Shon - page 134
 * **Laws of large numbers-**as you increase the numer of rimes a probability experiment is repeated the empirical probability (relative frequency) of an event approaches the theoretical probability of the event. For example in a sample of 1000 man you have ages between 25 and 34 and the frequency is 366, then the emopirical formula for a employer being that age is 366/1000 or 0.366. []
 * Tait - page 135-136 (thank you)

page 135: ~**Range Of Probability Rule:** The possibility of an event E is between 0 and 1 inclusive.

0 ≤ P(E) ≤ 1

Unlikely Likely [||-|]

Impossible Even Chance Certain

0.5

page 136:

~__**Complement of an event E**__: the set of all outcomes in a sample space that are not included in the event E. The completion of the event E is denoted by E and is read as "E Prime"

[]

=Chapter 3.3 Notes - Addition Rule ( By Jun) = http://www.youtube.com/watch?v=QE2uR6Z-NcU

http://www.mathgoodies.com/lessons/vol6/addition_rules.html

Alexia: Rolling a six sided die: If it rolls and lands on two and five. P(A or B) = P(A) + P(B) P(2) = (1/6) P(5) = (1/6) (1/6) + (1/6) = (2/6) = (1/3)

Shun: In a deck of cards, the probability of getting an ace is 1/13 and the probability of getting a king is also 1/13 SO... P(King and Ace)=0 P(King or Ace) = (1/13) + (1/13) = 2/13

When two events ("A" and "B") are Mutually Exclusive it is impossible for them to happen together: **P(A and B) = 0** //"The probability of A and B together equals 0 (impossible)"// But the probability of A **or** B is the sum of the individual probabilities:

**P(A or B) = P(A) + P(B)** //"The probability of A or B equals the probability of A plus the probability of B"//

//Lukas:// In poker, if a person needs two Aces to get a full house and there has only been one Ace dealt out of 15 cards, the probability of that person getting two Aces is 3/37.


 * Experiment 2: || A spinner has 4 equal sectors colored yellow, blue, green, and red. What is the probability of landing on red or blue after spinning this spinner? || [[image:http://www.mathgoodies.com/lessons/vol6/images/tab.gif width="20" height="1" caption=" "]] ||   ||
 * Probabilities: ||  || P(red) || = || __1__ ||
 * ^  ||^   || 4 ||
 * [[image:http://www.mathgoodies.com/lessons/vol6/images/tab.gif width="10" height="6" caption=" "]] ||
 * P(blue) || = || __1__ ||
 * ^  ||^   || 4 ||
 * [[image:http://www.mathgoodies.com/lessons/vol6/images/tab.gif width="10" height="6" caption=" "]] ||
 * P(red or blue) || = || P(red) || + || P(blue) ||
 * [[image:http://www.mathgoodies.com/lessons/vol6/images/tab.gif width="10" height="6" caption=" "]] ||
 * || = || __1__ || + || __1__ ||
 * ^  ||^   || 4 ||^   || 4 ||
 * ^  |||||||||| [[image:http://www.mathgoodies.com/lessons/vol6/images/tab.gif width="10" height="6" caption="  "]] ||
 * ^  ||   || __2__ ||
 * ^  ||^   || 4 ||
 * ^  || = || __1__ ||
 * ^  ||^   || 2 ||   ||
 * ^  ||^   || 2 ||   ||

Shon Using the addition rule. Let`s ay you select a card from a standard deck. Find the probality that the card is a 4 or an Ace. Solution:If the card is a 4, it cannot be an ace. So the events are mutually exclusive. The probability of getting a 4 or an Ace is P(4 or Ace) =p(4)+p(Ace)=4/52+4/52=8/52=2/13=o.154

=Chapter 3.4 Additional Topics in Probability and Counting=

Everyone in class must add something from the reading in this section. Please try not to repeat each other. Work collaboratively!

http://www.youtube.com/watch?v=D3FFewJCp-s (by Jun) Permutation: Ordered arrangement of objects. The number of different permutations of n distinct objests is n!. Permutations of n objects taken r at a time: where r is < or = n. Shon -Distingiushable permuations -of N objects, where n1 are of one type, N2 are of another type, and so on is.

.

Noah - COMBINATION OF n OBJECTS TAKEN r AT A TIME nCr = number of combinations of objects r = Objects n = group of objects

=Permutations and Combinations= If you have a collection of n distinguishable objects, then the number of ways you can pick a number r of them (r < n) is given by the permutation relationship: For example if you have six persons for tennis, then the number of pairings for singles tennis is But this really double counts, because it treats the a:b match as distinct from the b:a match for players a and b. So in only 15 matches you could produce all distinguishable pairings. If you don't want to take into account the different permutations of the elements, then you must divide the above expression by the number of permutations of r which is r!. This result is called a "combination". The combination relationship is. The number of tennis matches is then the combination Permutation: [] Combinations: []
 * [[image:http://hyperphysics.phy-astr.gsu.edu/hbase/math/immath/perm.gif align="center"]] ||  || [|Show] ||   ||