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Chapter 7: Probability

7.1 Randomness, Probability, and Simulation. Chapter 7: Probability. Definitions. Random-individual outcomes are uncertain, but given a large number of repetitions, a regular distribution appears Probability Experiment-action through which counts, measures, or responses are obtained

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Chapter 7: Probability

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  1. 7.1 Randomness, Probability, and Simulation Chapter 7: Probability

  2. Definitions • Random-individual outcomes are uncertain, but given a large number of repetitions, a regular distribution appears • Probability Experiment-action through which counts, measures, or responses are obtained • Sample Space-set of all possible outcomes • Event-subspace of sample space • Outcome-result of a single trial

  3. Examples • Probability experiment-rolling a die • Sample space {1,2,3,4,5,6} • Event {Die is even}={2,4,6} • Outcome {Die is a 4}={4} • Probability experiment-choosing a car off the production line • Sample space-all cars produced every where • Event-cars produced at the BMW plant in Spartanburg • Outcome-Z4 Roadster

  4. Definitions • The probability of all possible outcomes added together must equal 1. • Probability of an outcome-number between 0 and 1 • Outcomes with probability of 0 will never happen • Outcomes with probability of 1 will always occur • The probability of all other outcomes is calculated by Number of ways to get a desired outcome Total number of outcomes

  5. Coin Tossing • How many outcomes are possible for one coin flip? • What is the probability of getting a head? • How many outcomes are possible for two coins? • HH • HT • TH • TT • So what is the probability of getting two heads? • What is the probability of getting a head and a tails in any order?

  6. Coin Tossing • How many outcomes are possible with 3 coins? HHH HHT HTH HTT TTT TTH THT THH What is the probability of getting 2 tails and a head in any order?

  7. Rolling Dice • How many outcomes are possible for rolling one die? • What is the probability of getting a 3? • How many outcomes are possible when rolling two dice?

  8. Rolling Dice • What is the probability of getting an 8 when rolling 2 dice? • How many possible ways of getting an 8?

  9. Practice • What is the probability of rolling a 3 with two six-sided die? • What is the probability of getting two tails when tossing two coins? • When tossing 3 coins? • What number has the greatest probability of being rolled with two die?

  10. Homework (page 317) • 7.4 Probability is the measure of how likely an event is to occur. Match one of the probabilities that follow with each statement of likelihood given. 0 .01 .03 .6 .99 1 • This event is impossible. It can never occur. • This event is certain. It will occur on every trial. • This event is very unlikely but will occur once in a while in a long sequence of trials. • This event will occur more often than not.

  11. Homework (page 317) • 7.5 Imagine rolling a fair, six-sided die. What is the probability of getting a 4? Justify your answer.

  12. Homework (page 317) • 7.6 What is the probability of getting 2 heads and 1 tail when you toss three coins? Give appropriate evidence to support your answer.

  13. Examples of Real World Probability • Sports • Basketball • Shooting Technical Fouls • Football • Kicking a Field Goal • Baseball • Batting Averages

  14. Examples of Real World Probability • Medical Decisions • Surgeries • Treatments • Estimated Recovery Time

  15. Examples of Real World Probability • Insurance • Medical • Car • Home • Life

  16. Examples of Real World Probability • Casino/Lottery • Blackjack • 1/20 probability of getting a blackjack • Roulette • 1/38 chance of winning • MegaMillions • Until October 2013, odds of winning the jackpot were 1 in 175.7 million • Now odds of winning the jackpot are 1 in 258.9 million

  17. Examples of Real World Probability • Life Expectancy • Getting Loans • Weather

  18. Drawing Marbles • You have a bag with 10 marbles, 3 black, 3 red, 2 white, and 2 gray • What is the probability of drawing a red marble? • Total possibilities=10 • Favorable possibilities (red)=3 • Probability =3/10 • What is the probability of drawing a white? • Total possibilities=10 • Favorable possibilities (white)=2 • Probability= 2/10

  19. With/Without Replacement • Used for Drawing or Picking • With Replacement • Put back (replace) whatever you drew/picked • Without Replacement • Don’t put back (don’t replace) whatever you drew/picked

  20. Independent and Dependent Events • Independent Events • Two events that do not affect each other • Examples • Rolling two dice • Drawing two cards with replacement • Dependent Events • Events that do affect each other • Examples • Drawing two cards without replacement • Drawing marbles without replacement

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