Leon James and Diane Nahl posted results of a survey conducted in August 2000, where respondents were asked about various driving habits. This table classifies 1,086 participants according to type of car driven, and whether or not they were in the habit of making insulting gestures at other drivers. Notice that, unlike most tables encountered in this book, the explanatory variable (type of car) is indicated in columns and the response (gestures or not) is in rows.
a. Before calculating any conditional probabilities, identify the types of cars whose owners you would suspect to have a tendency to make insulting gestures at other drivers.
b. For each type of car, find the (conditional) probability that surveyed drivers of that type of car make insulting gestures.
c. Comment on whether or not your suspicions in part (a) were correct.
d. To three decimal places each, find the probability of driving a van (P(V)), the probability of making insulting gestures (P(G)), and the probability of driving a van and making insulting gestures (P(V and G)). e. Check if P(V and G) P(V) P(G) to see if the events V and G are independent, and explain the outcome. f. You found P(G given V) in part (b). Check if P(V and G) P(V) P(G given V) and explain the outcome. (It may help you to work with the original fractions instead of converting to decimals.)
g. Which would you suspect to be higher: the probability of making insulting gestures (P(G)), or the probability of making insulting gestures given that someone drives a sports car (P(G given S))? Report the two probabilities to three decimal places.
h. Find the overall probability of driving an economy car, a family car, a luxury car, or a van.
i. Find the probability of making insulting gestures, given that someone drives an economy car, a family car, a luxury car, or a van.
j. Are drivers of economy cars, family cars, luxury cars, and vans less likely in general to make insulting gestures?
k. Did the surveyors allow for overlapping of categories, in cases where someone drives more than one type of car?