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5.1 Introducing Probability

5.1 Introducing Probability. Objectives: By the end of this section, I will be able to… Understand the meaning of an experiment, an outcome, an event, and a sample space. Describe the classical method of assigning probability.

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5.1 Introducing Probability

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  1. 5.1 Introducing Probability Objectives: By the end of this section, I will be able to… • Understand the meaning of an experiment, an outcome, an event, and a sample space. • Describe the classical method of assigning probability. • Explain the Law of Large Numbers and the relative frequency method of assigning probability.

  2. Rules of Probability • Probabilities must be between 0 and 1. • For any experiment, the sum of all outcome probabilities must = 1

  3. Probability terms • Outcome: result of experiment. • Sample Space: all the possible outcomes of experiment

  4. PROBABILITY

  5. Experimental Probability vs. Theoretical Probability • Roll ONE die 15 times. • WRITE OUT your results. • What is your probability of rolling a FIVE? This is an example of experimental probability.

  6. ONE DIE THEORETICAL PROBABILITY 1) What is the probability that you will roll a 5? 1 __ = 1 ways 5 6

  7. TWO DICE • Two dice are rolled at the same time. Find the sample space. 5,1 5,2 5,3 5,4 5,5 5,6 6,1 6,2 6,3 6,4 6,5 6,6 1,1 1,2 1,3 1,4 1,5 1,6 2,1 2,2 2,3 2,4 2,5 2,6 2,1 3,1 3,2 3,3 3,4 3,5 3,6 4,1 4,2 4,3 4,4 4,5 4,6 1,2 36

  8. TWO DICE • With two dice, what is the probability that you will roll a seven? • With two dice, what is the probability that you will roll a number larger than 10? 3,4 6,1 1,6 2,5 5,2 4,3 = 6 ways 6 __ 36 3 __ 5,6 6,6 = 3 ways 11 12 36 6,5

  9. DECK OF CARDS 52 • How many cards are in a deck? • How many face cards are there? • How many suits are in a deck of cards? • How many cards are in each suit? 12 4 13

  10. A face card? A red two? DECK OF CARDSWhat is the probability of getting… 12 = # of face cards 52 = sample space 2 = # of red twos __ 52 = sample space

  11. Tree Diagrams • Draw a Tree Diagram to represent what can happen when you toss a coin.

  12. Tree Diagrams P(H) = P(H) = 1/2 H H T Toss a Coin P(H,H) = P(H,H) = ½ · ½ = ¼ H T T

  13. Use the following table to find the probability • Find the probability that a randomly selected worker at McDonalds 2) Is a college grad 3) Is a male 4) Is a male who graduated from Grad school 63 / 169 78 / 169 31 / 169 20 27 27 31 31 78 36 169 63

  14. Scenarios • A slot machine in VEGAS has three wheels, and each wheel has a picture of a lemon, cherry, and an apple on it. Each wheel operates independently of the other. When all three wheels show the same item, then the player wins $5000. • Find the probability of a player winning $5000 when playing this slot machine.

  15. Forgetful Students • Sallies students are very forgetful. Three of Mrs. Godfrey’s seniors left their calculators in her classroom. They all stop by after school at different times and randomly select a calculator. The calculators all look exactly the same too! What is the probability that they pick the correct one?

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