FUNDAMENTALS OF ALLGEBRA 2 A CHAPTER 11 POWERPOINT

FUNDAMENTALS OF ALLGEBRA 2 A CHAPTER 11 POWERPOINT PRESENTATION PERMUTATIONS, COMBINATIONS, AND PROBABILITY

LEARNING TARGETS • AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: • USE THE FUNDAMENTAL PRINCIPLE OF COUNTING • DETERMINE THE NUMBER OF PERMUTATIONS AND COMBINATIONS • FIND THE PROBABILITY OF EVENTS • USE BINOMIAL THEOREM • IDENTIFY SEQUENCES

CHAPTER VOCABULARY • TREE DIAGRAM: A CHART WITH BRANCHES THAT SHOW RELATIONSHIPS • FUNDEMENTAL PRINCIPLE OF COUNTING: COUNTING EVENTS: if one task can be completed (p) different ways and a second task can be completed (q) different ways, then the first task followed by the second can be completed in (pq) different ways. • MULTIPLICATION PRINCIPLE: THE FORMULA TOTAL NUMBER OF SELECTIONS IN SUCCESSION

TREE DIAGRAM

Fundamental Principle of Counting

MULTIPLICATION PRINCIPLE

PERMUTATIONS • PERMUATIONS: THE ARRANGEMENT OF OBJECTS IN A SPECIFIC ORDER.

PERMUTATION/COMBINATION FORMULA

Combinations • Combinations: An arrangement of a group of objects in which order is not important.

FORMULA FOR COMBINATIONS

Sample With Replacement • Suppose you have a bag of marbles: All togethere are 10 marbles: 3 are black, 4 are red, 2 are yellow, and 1 is green. • If you take a marble out and replace it, you will still have: • 3/10 it is black, 2/5 it is red, 1/5 it is yellow, and 1/10 it is green. The odds do not change when you replace the item you pulled.

BASIC PROBABILITY • EVENT: AN INDIVIDUAL OUTCOME OF ANY SPECIFIED COMBINATIONS OF OUTCOMES. • PROBABILITY FRACTION: THE NUMBER OF FAVORABLE OUTCOMES DIVIDED BY THE TOTAL NUMBER OF POSSIBLE OUTCOMES. • COMPELMENTARY EVENT: AN OUTCOME THAT CAN BE FAVORABLE OR UNFAVORABLE ACCOMPANYING A PARTICULAR EVENT.

SPINNERS, NUMBER CUBES, MARBLES IN BAGS, ETC. • PROBABILTY EVENTS CAN BE FOUND ON: SPINNERS, MARBLES IN BAGS, NUMBER CUBES(FORMERLY KNOWS AS DICE), LETTERS IN THE ALPHABET, ETC.

BINOMIAL THEOREM • A WAY TO WRITE COMBINATIONS:

PASCAL’S TRIANGLE • IF YOU WRITE COEFFICIENTS SEPARATELY, YOU WILL GET A BEAUTIFUL PATTERN KNOWN AS PASCAL’S TRIANGLE:

ARITHMETIC SEQUENCES: VOCABULARY • SEQUENCE: AN ORDERED LIST OF NUMBERS. • ARITHMETIC SEQUENCE: A SEQUENCE IN WHICH SUCCESSIVE TERMS DIFFER BY THE SAME NUMBER, (d), CALLED THE COMMON DIFFERENCE. • COMMON DIFFERENCE: THE CONSTANT, (d), ADDED TO A TERM IN AN ARITHMETIC SEQUENCE TO GET THE NEXT TERM.

MORE VOCABULARY • SERIES: THE INDICATED SUM OF THE TERMS OF A SEQUENCE. • DERIVATION: A SEQUENCE OF STATEMENTS THAT SHOWS A RESULT IS A CONSEQUENCE OF ACCEPTED STATEMEMENTS. • GEOMETRIC SEQUENCE: A SEQUENCE IN WHICH SUCCESSIVE TERMS DIFFER BY THE SAME RATIO (r), CALLED THE COMMON RATIO.

GEOMETRIC MEAN • GEOMETRIC MEAN: THE SQUARE ROOT OF THE PRODUCT OF TWO NUMBERS. THE GEOMETRIC MEAN BETWEEN A AND B, IS THE SQUARE ROOT OF AB. • YOU CAN ALWAYS CREATE A GEOMETRIC SEQUENCE OF THREE TERMS BY FINDING THE GEOMETRIC MEAN BETWEEN TWO NUMBERS.

SIGMA NOTATION • SIGMA IS A LETTER IN THE GREEK ALPHABET AND IT IS USED AS A SYMBOL FOR SUM. • A SUBSCRIPT IS USED TO SHOW THE FIRST TERM. • A SUPERSCRIPT IS USED TO SHOW THE LAST TERM.

Sigma Notation

TERMS • CONVERGENT SERIES: AN INFINITE SERIES WHOSE PARTIAL SUMS APPROACH A FIXED NUMBER AS (n) INCREASES. • DIVERGENT SERIES: AN INFINITE SERIES WHOSE PARTIAL SUMS DO NOT APPROACH A FIXED NUMBER AS (n) INCREASES.

I LOVE MATH! Permutations!!!!