Stat 100

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Stat 100

• Feb. 20

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Stat 100

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

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Thought Question

• A normal 52-card deck is randomly shuffled.
• What is the probability that the fourth card down
  is the Ace of Hearts?
• Answer1/52. Random shuffle gives any card the
  same chance to be in any spot.

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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.

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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 dont get the
  disease from first bite but get it from second
• (99/100)(1/100) 99/10,000

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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?

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Expected Value

• Mean outcome per trial in the long run
• List possible outcome values and their
  probabilities
• Exp Valuesum of (valueprobability)

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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

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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

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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

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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)
  (-999499)/1000 -0.50
• Interpretation On average, player lose 50 cents
  per game

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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