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Stat 100

Stat 100. Feb. 20. Stat 100. Read Ch. 15; Try 1-5, 7, 14, 17, 18, 21, 25 Read Chapter 16. Thought Question. A normal 52-card deck is randomly shuffled. What is the probability that the fourth card down is the Ace of Hearts?

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Stat 100

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  1. Stat 100 Feb. 20

  2. Stat 100 • Read Ch. 15; Try 1-5, 7, 14, 17, 18, 21, 25 • Read Chapter 16

  3. Thought Question • A normal 52-card deck is randomly shuffled. • What is the probability that the fourth card down is the Ace of Hearts? • Answer=1/52. Random shuffle gives any card the same chance to be in any spot.

  4. Problem 15.19 • Lyme disease is transmitted to humans by tick bites. Suppose the probability of contracting the disease is 1/100 for each tick bite.

  5. 15.19 continued • What is the probability you will not get the disease when bitten once? • 99/100 • What is the probability that if you are bitten twice, the result is that you don’t get the disease from first bite but get it from second • (99/100)(1/100) = 99/10,000

  6. Problem 15.18 • You routinely check coin-return slots in vending machines to see if they have any money in them. • About 10% of the time you find money. • What is the probability that you do not find money the next time you check? • What is the probability that the next time you will find money is on the third try? • What is the probability that you will have found money by the third try?

  7. Expected Value • Mean outcome per trial in the long run • List possible outcome values and their probabilities • Exp Value=sum of (value×probability)

  8. Problem 15.25 continued • In 1991, in the U.S.: • 72% of children lived with both parents • 22% lived with mother only • 3% lived with father only • 3% lived with neither parent

  9. Part a • What is the expected value for the number of parents a randomly selected child is living with? • (2)(.72) + (1)(.22) + (1)(.03) + (0)(03) = • 1.69

  10. 15.25 continued • Does the concept of expected value have a meaningful interpretation for this example? • Debatable, but the “No” answer would be that nobody lives with 1.69 parents • The value 1.69 is the average over all children in the country

  11. Pennsylvania Daily number • 999/1000 chance of losing $1 • 1/1000 chance of winning $499 • What is the “expected value” of the game? • (999/1000)(-1) + (1/1000)(499) = (-999+499)/1000 = -0.50 • Interpretation: On average, player lose 50 cents per game

  12. Fair Game • Explain why the PA Daily number game is not fair • State has the advantage in the long run • Will average out to a gain of 50 cents per play for the state. • Definition of fair game: Expected value = 0

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