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1-1 Objectives

This lesson introduces students to the basic concepts of probability, including randomness, combined probability, dependent and independent events, and the gambler's fallacy. Students will learn how to calculate probabilities and apply them to real-world scenarios. The lesson also explores the concept of batting average and its relevance to probability.

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1-1 Objectives

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  1. 1-1Objectives Introduce students to the basic concepts of probability, including: • randomness • combined probability • dependent events • independent events • gambler’s fallacy

  2. 1-2Defining Probability Probability is A. the likelihood that a given event will occur B. A number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences(Soukhanov, 1992)

  3. 1-3Probability of rolling a “1” (# of favorable results)  (# of possible results) = 1/6 A "favorable result" is the result for which you are determining the probability. In this case, you are determining the probability of a single event 1/6 = .17 = 17%

  4. 1-4Randomness • Each possible outcome in that process has the same chance, or probability, of occurring • Outcomes are determined by chance

  5. 1-5Probability in the Real World Probability = # Favorable Outcomes Total # Trials Probabilities based on trials are an estimate

  6. 1-6Combined Probability Probability of the 1st event AND 2nd event occurring Probability of 1st event X Probability of 2nd event Combined Probability

  7. 1-7Is an Event Dependent or Independent? INDEPENDENT The outcome of the 1st event does not affect the outcome of the 2nd event DEPENDENT The outcome of the 1st event does affect the outcome of the 2nd event

  8. 1-8Gambler’s Fallacy Mistaking independent events for dependent events In reality, the outcomes are completely independent

  9. 1-9Probability of One Event vs. a Group of Events Assumption: Outcome is Random Probability of 1st x 2nd x 3rd x 4th = Combined Probability of a group of events

  10. 1-10SharedBirthdays With any group of 23 people, there is a 50% chance that two or more people in that group will have the same birthday

  11. 1-11Heads or Tails? In your group, flip the coin 20 times Each group will record the results • count the number of heads and tails • calculate the percentage of heads

  12. 1-12Outcome and Probability What are all the possible outcomes for flipping two coins? heads/heads heads/tails tails/heads tails/tails What are the probabilities of each outcome?

  13. 1-13Becoming a Legend Batting Average calculated # Hits during season Total # times at bat .400 batting avg. means a hit 4 out of 10 times at bat 1941: Ted Williams approached the last day of play with a .39955 (179/448) The Red Sox coach offered to let Williams sit out the last day to avoid slipping below .400

  14. 1-14Becoming a Legend: Part II • Given Ted Williams batting average before the last day (.39955), how many hits would you expect him to get out of 8 times at bat? • If Williams went to bat 8 times on his final day and got the number of hits calculated above, what would his season average have been? • Would you have played the last games or sat them out?

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