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Chapter Five

Chapter Five. 5.1 Probability in our Daily Lives. What is Random?. Which of these list is a “random” list of results when flipping a fair coin 10 times? A) T H T H T H T H T H B) T T H T H T T H H T C) H H H H H H H H H Answer: D) All of the above!. Probability:.

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Chapter Five

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  1. Chapter Five 5.1 Probability in our Daily Lives

  2. What is Random? • Which of these list is a “random” list of results when flipping a fair coin 10 times? • A) T H T H T H T H T H • B) T T H T H T T H H T • C) H HHHHHHHH • Answer: D) All of the above!

  3. Probability: • With a small number of trials the outcome of random events can vary widely from what we expect them to be. • Examples: • Coin Flips • Winning Streaks • Others

  4. Probability: • However with a Large number of event, Called Trials, the proportion of times the event occurs will become more predictable. • Examples: • Casino games • Others

  5. Law of Large Numbers: • With a randomized experiment, the probability of a particular outcome is the proportion of times that outcome would occur in a long run of observations. • Outcome: The result of a specific trial. • Long run: Very large, often theoretically large, number of trials.

  6. Independence: • We are going to try a few coin flips: • Flip One: Tails • Flip Two: Heads • Flip Three: Heads • Flip Four: Heads • Flip Five: Heads • Flip six: Heads • No matter what happened before the odds will always be 50::50.

  7. Independent Trials: • Different trials of a random phenomenon are independent if the outcome of any one trial is not effected by the outcome of any other trial. Independent Examples: Dependent Examples:

  8. Finding Probabilities: • 1) Logic, symmetry, structure. • Best for simple well understood situations. • 2) Sample trials. • Good for complex situations we can model.

  9. Next Time Finding Probabilities. “What is the chance of rolling at least one 6 on six roles?”

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