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