# 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