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?
• Answer=1/52. Random shuffle gives any card the same chance to be in any spot.
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.
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
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
Expected Value
• Mean outcome per trial in the long run
• List possible outcome values and their probabilities
• Exp Value=sum of (value×probability)
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
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
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
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
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
