Chapter 6 Warm Ups
1) Vehicles. Suppose that 46% of families living in a certain county own a car and 18% own an SUV. The Addition Rule might suggest, then, that 64% of families own either a car or an SUV. What’s wrong with that reasoning?
1) Vehicles. Suppose that 46% of families living in a certain county own a car and 18% own an SUV. The Addition Rule might suggest, then, that 64% of families own either a car or an SUV. What’s wrong with that reasoning? A family may have both a car and an SUV. The events are not disjoint, so the Addition Rule does not apply.
2) Speeders. Traffic checks on a certain section of highway suggest that 60% of drivers are speeding there. Since 0.6 x 0.6 = 0.36, the Multiplication Rule might suggest that there’s a 36% chance that two vehicles in a row are both speeding. What’s wrong with that reasoning?
2) Speeders. Traffic checks on a certain section of highway suggest that 60% of drivers are speeding there. Since 0.6 x 0.6 = 0.36, the Multiplication Rule might suggest that there’s a 36% chance that two vehicles in a row are both speeding. What’s wrong with that reasoning? When cars are traveling close together, their speeds are not independent. For example, a car following directly behind another can’t be going faster that the car ahead. Since the speeds are not independent, the Multiplication Rule does not apply.
3) Lefties. Although it’s hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since 0.14 x 0.14 = 0.0196, the Multiplication Rule might suggest that there’s about a 2% chance that a brother and a sister are both lefties. What’s wrong with that reasoning?
3) Lefties. Although it’s hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since 0.14 x 0.14 = 0.0196, the Multiplication Rule might suggest that there’s about a 2% chance that a brother and a sister are both lefties. What’s wrong with that reasoning? There may be a genetic factor making handedness of siblings not independent. The Multiplication Rule does not apply.