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Probability and Statistics

Probability and Statistics. Chapter 12. Multiplication Counting Principle. (The Fundamental Counting Principle) Multiply the number of choices for each Example: You have a five shirts and three pairs of pants. How many outfits do you have?. Pant choices. Shirt choices. Examples:.

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Probability and Statistics

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  1. Probability and Statistics Chapter 12

  2. Multiplication Counting Principle (The Fundamental Counting Principle) Multiply the number of choices for each Example: You have a five shirts and three pairs of pants. How many outfits do you have? Pant choices Shirt choices

  3. Examples: • A restaurant has 4 appetizers, 8 main courses, and 3 desserts. How many different dinners are available? • A pizza shop offers 8 vegetable toppings and 6 meat toppings. How many different pizzas can you make with one of each topping?

  4. Factorial n! Multiply the values 1 – n Example: 4! = 4 x 3 x 2 x 1 = 24

  5. Examples: Find the value • 5! • 7! • Find 12! using the calculator In the Calculator: Go to MATH, PRB, and choose 4

  6. Permutation • An arrangement of objects in a specific order Example: If you are arranging the letters A, B, and C without repeating the letters, how many ways can they be arranged? ABC, ACB, BAC, BCA, CAB, CBA ORDER MATTERS!!!!

  7. Permutation notation: nPr Where n is the number of objects and r is how many objects are being arranged

  8. Example • You have 8 books and are arranging 3 of them on a shelf. How many ways can you arrange the three books. n = the number of objects n = 8 r = how many are being arranged r = 3

  9. Calculating nPr

  10. Example • There are 12 different songs that the Spring Chorus can choose from. How many ways can they perform 4 of the songs?

  11. Example • There are 6 boys in the class. Three of the boys are going to the board to do homework problems. How many ways can the boys be called to the board?

  12. Combination • An arrangement of objects in where order does not matter Example: If you are arranging the letters A, B, and C without repeating the letters, how many ways can they be arranged? ABC, ACB, BAC, BCA, CAB, CBA are all the same!! So there is only 1 way! ORDER Doesn’t MATTER!!!!

  13. Combination notation: nCr Where n is the number of objects and r is how many objects are being arranged

  14. Example • You have 8 books and are arranging 3 of them on a shelf. How many ways can you arrange the three books where order does not matter? n = the number of objects n = 8 r = how many are being arranged r = 3

  15. Calculating nPr Removes the repeats!

  16. Example • There are 12 different songs that the Spring Chorus can choose from. How many combinations of 4 songs can they perform?

  17. Example • There are 6 boys in the class. Three of the boys are going to the board to complete the same problem. How many ways can the boys be called to the board considering they are all doing the same problem?

  18. Probability • How likely it is that an event with occur Notation: P(event) Example: What is the probability that you will roll a 5 on a fair dice? Outcome – the result of a single trial 5 Sample Space – all possible outcomes 1, 2, 3, 4, 5, 6 Event – the outcome P(5) =

  19. Probability can be represented as a fraction, or decimal and is always between 0 and 1. P(5) = = .167 certain Equally likely impossible Less likely More likely How likely is it that a 5 will be rolled? Less likely

  20. Theoretical Probability • Probability based on equally likely outcomes • Example: Rolling the dice for a 5 provides a theoretical probability of

  21. Experimental Probability • Probability based on data collected • Example: Rolling the dice six different times. How many times did you roll a 5?

  22. Example: • Find the theoretical probability of flipping tails on a coin. • Flip the coin ten times. What is the experimental probability? • How do they compare?

  23. Complement of an event • The probability of all the outcomes that are not in the event P(event) + P(not event) = 1 P(5) + P(not 5) = 1

  24. In a deck of cards, what is the probability that the you will be dealt a card that is not a heart? P(heart) P(not heart)

  25. In a deck of cards, what is the probability that the you will be dealt a card that is not a queen? P(queen) P(not queen)

  26. Leave as a fraction Finding the odds Ratio that compares the favorable vs. unfavorable outcomes. Odds in favor of an event = Odds against an event =

  27. What are the odds that you will roll a 5 on a dice? Favorable Events = 5 # Favorable Events = 1 Unfavorable Events = 1, 2, 3, 4, 6 # Unfavorable Events = 5

  28. What are the odds that you will not roll a 5 on a dice? Favorable Events = 1, 2, 3, 4, 6 # Favorable Events = 5 Unfavorable Events = 5 # Unfavorable Events = 1

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