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FUNDAMENTALS OF ALLGEBRA 2A CHAPTER 11 POWERPOINT PRESENTATION

FUNDAMENTALS OF ALLGEBRA 2A 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

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FUNDAMENTALS OF ALLGEBRA 2A CHAPTER 11 POWERPOINT PRESENTATION

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  1. FUNDAMENTALS OF ALLGEBRA 2ACHAPTER 11 POWERPOINT PRESENTATION PERMUTATIONS, COMBINATIONS, AND PROBABILITY

  2. 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

  3. 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

  4. TREE DIAGRAM

  5. Fundamental Principle of Counting

  6. MULTIPLICATION PRINCIPLE

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

  8. PERMUTATION/COMBINATION FORMULA

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

  10. FORMULA FOR COMBINATIONS

  11. Sample With Replacement • Suppose you have a bag of marbles: All together there 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.

  12. 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.

  13. 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.

  14. BINOMIAL THEOREM • A WAY TO WRITE COMBINATIONS:

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

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. Sigma Notation

  21. 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.

  22. I LOVE MATH!Permutations!!!!

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